iProver---3.9.4.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWV990-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n008.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 : Fri Sep 25 03:24:34 PM UTC 2026

% Result   : Unsatisfiable 138.77s 20.96s
% Output   : CNFRefutation 147.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :  306
% Syntax   : Number of formulae    : 8726 (2620 unt;   5 def)
%            Number of atoms       : 49537 (1381 equ)
%            Maximal formula atoms :    7 (   5 avg)
%            Number of connectives : 17215 (7325   ~;9890   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   6 prp; 0-5 aty)
%            Number of functors    :   73 (  73 usr;  15 con; 0-5 aty)
%            Number of variables   : 59589 (   0 sgn59589   !;   0   ?;57737   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | c_Value_Oval_OAddr(X0) != c_Value_Oval_OAddr(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).

fof(f4,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBlockThrow_0) ).

fof(f5,axiom,
    ! [X0] : c_Value_Oval_OUnit != c_Value_Oval_OAddr(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I10_J_0) ).

fof(f6,plain,
    ! [X0] : c_Value_Oval_OAddr(X0) != c_Value_Oval_OUnit,
    inference(reorient_equations,[],[f5]) ).

fof(f7,axiom,
    ! [X0] : c_Value_Oval_ONull != c_Value_Oval_OAddr(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I16_J_0) ).

fof(f8,plain,
    ! [X0] : c_Value_Oval_OAddr(X0) != c_Value_Oval_ONull,
    inference(reorient_equations,[],[f7]) ).

fof(f9,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).

fof(f13,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).

fof(f17,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OFAss(X4,X5,X6,X7,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).

fof(f19,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).

fof(f20,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBlock(X4,X5,X6,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3),
    inference(reorient_equations,[],[f19]) ).

fof(f24,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).

fof(f27,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OBlock(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).

fof(f28,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBlock(X3,X4,X5,X2) != c_Expr_Oexp_OWhile(X0,X1,X2),
    inference(reorient_equations,[],[f27]) ).

fof(f29,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).

fof(f30,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OBlock(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).

fof(f31,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBlock(X3,X4,X5,X2) != c_Expr_Oexp_OCast(X0,X1,X2),
    inference(reorient_equations,[],[f30]) ).

fof(f35,axiom,
    c_Value_Oval_ONull != c_Value_Oval_OUnit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I5_J_0) ).

fof(f36,plain,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    inference(reorient_equations,[],[f35]) ).

fof(f37,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OBlock(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).

fof(f38,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBlock(X3,X4,X5,X2) != c_Expr_Oexp_OSeq(X0,X1,X2),
    inference(reorient_equations,[],[f37]) ).

fof(f39,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).

fof(f40,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBlock(X4,X5,X6,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3),
    inference(reorient_equations,[],[f39]) ).

fof(f41,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).

fof(f42,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OVal(X0,X1) != c_Expr_Oexp_OBlock(X2,X3,X4,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

fof(f43,plain,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OBlock(X2,X3,X4,X1) != c_Expr_Oexp_OVal(X0,X1),
    inference(reorient_equations,[],[f42]) ).

fof(f44,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).

fof(f45,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OBlock(X4,X5,X6,X3) != c_Expr_Oexp_OBlock(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f44]) ).

fof(f46,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).

fof(f47,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OBlock(X4,X5,X6,X3) != c_Expr_Oexp_OBlock(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f46]) ).

fof(f48,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).

fof(f49,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OBlock(X4,X5,X6,X3) != c_Expr_Oexp_OBlock(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f48]) ).

fof(f50,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OTryCatch(X4,X5,X6,X7,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).

fof(f51,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).

fof(f52,axiom,
    ! [X2,X0,X1] :
      ( X0 = X2
      | c_Expr_Oexp_OVal(X0,X1) != c_Expr_Oexp_OVal(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

fof(f64,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

fof(f67,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).

fof(f69,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OVal(X5,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

fof(f70,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X2)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).

fof(f71,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_OVal(X0,X1) != c_Expr_Oexp_OWhile(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).

fof(f72,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

fof(f74,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_Othrow(X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).

fof(f77,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).

fof(f78,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OWhile(X4,X5,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3),
    inference(reorient_equations,[],[f77]) ).

fof(f80,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OWhile(X5,X6,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).

fof(f81,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).

fof(f82,plain,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OVal(X4,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3),
    inference(reorient_equations,[],[f81]) ).

fof(f87,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OVal(X5,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

fof(f88,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).

fof(f89,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OWhile(X4,X5,X3) != c_Expr_Oexp_OCond(X0,X1,X2,X3),
    inference(reorient_equations,[],[f88]) ).

fof(f90,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OVal(X0,X1) != c_Expr_Oexp_OCond(X2,X3,X4,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

fof(f91,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

fof(f92,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).

fof(f93,axiom,
    ! [X2,X3,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedWhile_0) ).

fof(f94,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X2,X3)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).

fof(f95,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_WellTypeRT_OWTrt(X0,X5,X2,X3,X4)
      | ~ c_Objects_Ohext(X5,X1)
      | c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

fof(f96,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Objects_Ohext(X0,X2)
      | ~ c_Objects_Ohext(X2,X1)
      | c_Objects_Ohext(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).

fof(f98,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_List_Olist__all2(c_Conform_Oconf(X0,X5,X2),X3,X4,tc_Value_Oval,tc_Type_Oty)
      | ~ c_Objects_Ohext(X5,X1)
      | c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X4,tc_Value_Oval,tc_Type_Oty) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__hext_0) ).

fof(f99,axiom,
    ! [X0] : c_Objects_Ohext(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).

fof(f100,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_Objects_Ohext(X5,X1)
      | ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X5,X2),X3),X4))
      | hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X1,X2),X3),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__hext_0) ).

fof(f101,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

fof(f102,axiom,
    ! [X2,X0,X1] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Wellfounded_Oacc(X0,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

fof(f103,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).

fof(f104,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OWhile(X4,X5,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3),
    inference(reorient_equations,[],[f103]) ).

fof(f105,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

fof(f106,plain,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OVal(X4,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3),
    inference(reorient_equations,[],[f105]) ).

fof(f107,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X0 = X3
      | c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).

fof(f108,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X4
      | c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).

fof(f109,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).

fof(f110,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).

fof(f111,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

fof(f112,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X2)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).

fof(f113,axiom,
    ! [X2,X0,X1] : c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_OVal(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

fof(f114,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OFAss(X3,X4,X5,X6,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).

fof(f115,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I65_J_0) ).

fof(f116,axiom,
    ! [X2,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedCastNull_0) ).

fof(f117,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsNull_0) ).

fof(f118,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),c_Expr_Oexp_OVal(X3,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).

fof(f119,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
      | ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
      | c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a)
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).

fof(f120,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
      | ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
      | hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).

fof(f121,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
      | ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
      | c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a)
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).

fof(f122,axiom,
    ! [X2,X0,X1] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X0,X2),X0,X2,X2),X1,tc_prod(X2,X2))
      | c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

fof(f123,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X3,t_a),t_a)
      | ~ c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X3),t_a,t_a),X3,tc_prod(t_a,t_a))
      | hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).

fof(f124,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(X1,c_Wellfounded_Oacc(X3,X4),X4)
      | ~ c_in(c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X3,X4),X4,X4),X3,tc_prod(X4,X4))
      | hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).

fof(f125,axiom,
    ! [X2,X0,X1] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

fof(f126,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X0,c_Relation_ORange(X1,X3,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

fof(f127,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X0,c_Relation_ORange(X1,X3,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

fof(f128,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_List_Olist__all2(c_Conform_Oconf(X0,X3,X1),X4,X2,tc_Value_Oval,tc_Type_Oty)
      | c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),c_Conform_Osko__Conform__Xconfs__conv__map__1__1(X0,X2,X3,X4,X1),X2,tc_Type_Oty,tc_Type_Oty) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__conv__map_1) ).

fof(f129,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X2,c_Pair(X0,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X1,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_Objects_Ohext(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

fof(f130,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed2_0) ).

fof(f131,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

fof(f132,axiom,
    ! [X2,X3,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).

fof(f133,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

fof(f134,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WhileRedsThrow_0) ).

fof(f137,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow2_0) ).

fof(f138,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).

fof(f139,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp2Reds_0) ).

fof(f140,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds2_0) ).

fof(f141,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X7,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X1,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds2_0) ).

fof(f142,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryRedsVal_0) ).

fof(f143,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X8,tc_List_Olist(tc_String_Ochar)),X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X2,X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow2_0) ).

fof(f144,axiom,
    ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X9,tc_List_Olist(tc_String_Ochar)),X8,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X3,X8,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow2_0) ).

fof(f145,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X1,X5,X6,X4)
      | c_TypeSafe__Mirabelle_Owf__config(X0,X1,X2,X3,v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X1,X0,X4,X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Subject__reduction_0) ).

fof(f146,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X1,X5,X6,X2)
      | hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X1,X0,X2,X3,X4)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Subject__reduction_1) ).

fof(f147,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,c_Pair(X5,X7,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X1,X8,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X2,c_Pair(X5,X7,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_WellTypeRT_OWTrt(X0,X5,X2,X6,X4)
      | c_WellTypeRT_OWTrt(X0,X1,X2,X3,v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X2,X0,X4,X3,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction2_0) ).

fof(f148,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,c_Pair(X5,X7,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X8,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X1,c_Pair(X5,X7,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_WellTypeRT_OWTrt(X0,X5,X1,X6,X2)
      | hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X1,X0,X2,X3,X4)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction2_1) ).

fof(f149,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellTypeRT_OWTrt(X0,X1,X2,X3,X6)
      | ~ c_WellTypeRT_OWTrt(X0,X1,X2,X4,X5)
      | c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OSeq(X3,X4,tc_List_Olist(tc_String_Ochar)),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

fof(f150,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X4
      | c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OLAss(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

fof(f151,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X0 = X3
      | c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OLAss(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

fof(f155,axiom,
    ! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

fof(f163,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X0,X1,tc_prod(X2,X2))
      | c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

fof(f166,axiom,
    ! [X2,X0,X1] : c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X2),X2,X1) = c_Relation_ORange(X0,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).

fof(f173,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).

fof(f174,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

fof(f175,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

fof(f177,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X3 = X8
      | c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

fof(f178,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X2 = X7
      | c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

fof(f179,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X1 = X6
      | c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).

fof(f180,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X0 = X5
      | c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

fof(f181,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

fof(f182,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).

fof(f183,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OBinOp(X4,X5,X6,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f182]) ).

fof(f184,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).

fof(f185,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OBinOp(X4,X5,X6,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f184]) ).

fof(f186,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).

fof(f187,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OBinOp(X4,X5,X6,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f186]) ).

fof(f189,axiom,
    c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf_0) ).

fof(f193,axiom,
    ! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

fof(f194,plain,
    ! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),
    inference(reorient_equations,[],[f193]) ).

fof(f197,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OTryCatch(X3,X4,X5,X6,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

fof(f199,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X2,X3,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X2,X3,X4),X4,X4),X3,tc_prod(X4,X4))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).

fof(f200,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X2,X3,X4),X4,X4),X3,tc_prod(X4,X4))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).

fof(f201,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).

fof(f202,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

fof(f203,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

fof(f205,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

fof(f206,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

fof(f207,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X1,X0,X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2))
      | c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

fof(f209,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
      | c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

fof(f210,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_Relation_Osingle__valued(X5,X3,X4)
      | ~ c_in(c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4))
      | ~ c_in(c_Pair(X2,X1,X3,X4),X5,tc_prod(X3,X4))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).

fof(f211,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

fof(f212,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow1_0) ).

fof(f213,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X5,X6,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X2,X3,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X5,c_Map_Omap__add(X2,X6,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__lcl__add_0) ).

fof(f214,axiom,
    ! [X2,X3,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

fof(f215,axiom,
    ! [X2,X3,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

fof(f216,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

fof(f217,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

fof(f218,axiom,
    ! [X2,X3,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

fof(f219,axiom,
    ! [X2,X3,X0,X1,X4] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

fof(f220,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X2,X5)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X5),X2,X6,X4)
      | c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X2,X0,X4,X3,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

fof(f221,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqRedsThrow_0) ).

fof(f222,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow1_0) ).

fof(f223,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRedsThrow_0) ).

fof(f224,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsThrow_0) ).

fof(f225,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondRedsThrow_0) ).

fof(f229,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAcc(X5,X6,X7,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

fof(f230,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).

fof(f231,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OSeq(X4,X5,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3),
    inference(reorient_equations,[],[f230]) ).

fof(f241,axiom,
    ! [X2,X0,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

fof(f247,axiom,
    ! [X2,X3,X0,X1,X4] : c_Map_Omap__add(X0,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) = c_Map_Omap__add(c_Map_Omap__add(X0,X1,X3,X4),X2,X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

fof(f248,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X0 = X5
      | c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

fof(f249,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X1 = X6
      | c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

fof(f250,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X2 = X7
      | c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

fof(f251,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X3 = X8
      | c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

fof(f252,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).

fof(f253,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

fof(f254,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

fof(f255,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

fof(f256,axiom,
    ! [X0,X1] : c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1) = c_Relation_OId__on(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

fof(f257,plain,
    ! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),
    inference(reorient_equations,[],[f256]) ).

fof(f258,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

fof(f259,plain,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_Othrow(X4,X3) != c_Expr_Oexp_OCond(X0,X1,X2,X3),
    inference(reorient_equations,[],[f258]) ).

fof(f261,axiom,
    ! [X0,X1] : c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

fof(f265,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).

fof(f266,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBinOp(X4,X5,X6,X3) != c_Expr_Oexp_OCond(X0,X1,X2,X3),
    inference(reorient_equations,[],[f265]) ).

fof(f267,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_Othrow(X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).

fof(f268,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).

fof(f269,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCast(X4,X5,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3),
    inference(reorient_equations,[],[f268]) ).

fof(f270,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

fof(f273,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).

fof(f274,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OFAcc(X4,X5,X6,X3) != c_Expr_Oexp_OBinOp(X0,X1,X2,X3),
    inference(reorient_equations,[],[f273]) ).

fof(f277,axiom,
    ! [X0,X1] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

fof(f278,plain,
    ! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),
    inference(reorient_equations,[],[f277]) ).

fof(f279,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

fof(f280,axiom,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

fof(f283,axiom,
    ! [X2,X0,X1] :
      ( X0 = X2
      | c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_Othrow(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

fof(f284,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OCond(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

fof(f286,axiom,
    ! [X0,X1] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

fof(f289,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCast(X5,X6,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

fof(f290,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OFAss(X3,X4,X5,X6,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

fof(f291,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

fof(f292,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCast(X4,X5,X3) != c_Expr_Oexp_OCond(X0,X1,X2,X3),
    inference(reorient_equations,[],[f291]) ).

fof(f293,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

fof(f294,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCall(X5,X6,X7,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

fof(f295,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

fof(f296,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCall(X4,X5,X6,X3) != c_Expr_Oexp_OCond(X0,X1,X2,X3),
    inference(reorient_equations,[],[f295]) ).

fof(f297,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAcc(X5,X6,X7,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

fof(f300,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_OSeq(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

fof(f301,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OLAss(X5,X6,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

fof(f302,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OCall(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

fof(f303,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OFAcc(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

fof(f304,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).

fof(f307,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OFAcc(X3,X4,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

fof(f308,axiom,
    ! [X0,X1] : c_Relation_ODomain(c_Relation_OId__on(X0,X1),X1,X1) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

fof(f309,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_OTryCatch(X2,X3,X4,X5,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

fof(f310,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

fof(f311,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X0 = X4
      | c_Expr_Oexp_OCall(X4,X5,X6,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f310]) ).

fof(f312,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

fof(f313,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X1 = X5
      | c_Expr_Oexp_OCall(X4,X5,X6,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f312]) ).

fof(f314,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

fof(f315,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( X2 = X6
      | c_Expr_Oexp_OCall(X4,X5,X6,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3) ),
    inference(reorient_equations,[],[f314]) ).

fof(f316,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OTryCatch(X4,X5,X6,X7,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

fof(f318,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Relation_Orefl__on(X0,X1,X2)
      | c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

fof(f319,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2)
      | c_Relation_Orefl__on(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

fof(f320,axiom,
    ! [X2,X3,X0,X1] : c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_OCast(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

fof(f321,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_OCall(X2,X3,X4,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

fof(f323,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).

fof(f324,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_OBinOp(X2,X3,X4,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).

fof(f325,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X0 = X3
      | c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

fof(f326,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X4
      | c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

fof(f327,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCond(X5,X6,X7,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

fof(f328,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OFAss(X4,X5,X6,X7,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

fof(f329,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OFAss(X4,X5,X6,X7,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3),
    inference(reorient_equations,[],[f328]) ).

fof(f330,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_Othrow(X5,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

fof(f331,axiom,
    ! [X0,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ODomain(X0,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

fof(f332,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OTryCatch(X4,X5,X6,X7,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).

fof(f333,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).

fof(f334,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X0 = X3
      | c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

fof(f335,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X4
      | c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

fof(f336,axiom,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

fof(f337,plain,
    ! [X2,X3,X0,X1,X4,X5] : c_Expr_Oexp_OCast(X4,X5,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3),
    inference(reorient_equations,[],[f336]) ).

fof(f338,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OFAss(X3,X4,X5,X6,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

fof(f339,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OBinOp(X5,X6,X7,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).

fof(f340,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OTryCatch(X3,X4,X5,X6,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

fof(f341,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

fof(f342,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : c_Expr_Oexp_OFAcc(X4,X5,X6,X3) != c_Expr_Oexp_OCall(X0,X1,X2,X3),
    inference(reorient_equations,[],[f341]) ).

fof(f343,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

fof(f344,axiom,
    ! [X2,X3,X0,X1,X4] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

fof(f345,axiom,
    ! [X0,X1] : c_Relation_Osingle__valued(c_Relation_OId__on(X0,X1),X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

fof(f346,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsThrowObj_0) ).

fof(f347,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X5,X6,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X2,X3,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X5,c_Map_Omap__add(X2,X6,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__lcl__add_0) ).

fof(f348,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccRedsThrow_0) ).

fof(f349,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X5,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow1_0) ).

fof(f351,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_Relation_Orefl__on(X1,X4,X2)
      | ~ c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))
      | c_in(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

fof(f352,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_Relation_Orefl__on(X1,X4,X2)
      | ~ c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))
      | c_in(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

fof(f353,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_Relation_Orefl__on(X3,X2,X1)
      | ~ c_in(X0,X3,X1)
      | c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

fof(f356,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(X0,X3,X2,X4),c_Product__Type_OSigma(X1,X5,X2,X4),tc_prod(X2,X4))
      | c_in(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

fof(f357,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(X2,X0,X4,X3),c_Product__Type_OSigma(X5,X1,X4,X3),tc_prod(X4,X3))
      | c_in(X0,hAPP(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

fof(f359,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(X1,X2,X3),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

fof(f361,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3))
      | c_in(X0,c_Relation_ORange(X1,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).

fof(f364,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X0,X2,X1)
      | c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId__on(X2,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

fof(f365,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X3,X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
      | c_in(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

fof(f367,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(X5,X2,X3)
      | ~ c_in(c_Pair(X5,X0,X3,X4),X1,tc_prod(X3,X4))
      | c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

fof(f369,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).

fof(f371,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(X0,X4,X2)
      | ~ c_in(X1,hAPP(X5,X0),X3)
      | c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

fof(f372,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X2,X5)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X5),X2,X6,X4)
      | c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X2,X0,X4,X3,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__preserves__type_1) ).

fof(f373,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X1,X5)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X5),X1,X6,X2)
      | hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X1,X0,X2,X3,X4)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_1) ).

fof(f374,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).

fof(f375,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

fof(f376,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | X0 = X1
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).

fof(f377,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X2,X3,X4)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).

fof(f378,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | X1 = X0
      | c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).

fof(f379,plain,
    ! [X2,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | X0 = X1
      | c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(reorient_equations,[],[f378]) ).

fof(f380,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).

fof(f383,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | X0 = X1
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).

fof(f384,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).

fof(f385,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).

fof(f386,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | X1 = X0
      | c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).

fof(f387,plain,
    ! [X2,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | X0 = X1
      | c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(reorient_equations,[],[f386]) ).

fof(f388,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).

fof(f389,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X2,X3,X4)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).

fof(f390,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X2,X1,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X2,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).

fof(f391,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).

fof(f392,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

fof(f393,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

fof(f394,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X2,X3,X4),X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).

fof(f395,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X2,X3,X4)))
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).

fof(f396,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X2,X3,X3),c_Transitive__Closure_Ortrancl(X1,X3),tc_prod(X3,X3))
      | X0 = X2
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X1,X0,X2,X3),X3,X3),X1,tc_prod(X3,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).

fof(f397,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3))
      | X1 = X2
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X0,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).

fof(f398,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | X0 = X1
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).

fof(f399,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X6,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X1,X5)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X5),X1,X6,X2)
      | hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X1,X0,X2,X3,X4)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__preserves__type_0) ).

fof(f400,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X5,tc_Value_Oval,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X2),X5,X4,tc_Type_Oty,tc_Type_Oty)
      | c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X4,tc_Value_Oval,tc_Type_Oty) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__widens_0) ).

fof(f401,axiom,
    ! [X2,X3,X0,X1] :
      ( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

fof(f404,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).

fof(f405,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ hBOOL(hAPP(X5,X0))
      | ~ c_in(c_Pair(X1,X4,X3,X3),hAPP(X6,X0),tc_prod(X3,X3))
      | c_in(c_Pair(c_Pair(X0,X1,X2,X3),c_Pair(X0,X4,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Recdef_Osame__fst(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__fstI_0) ).

fof(f406,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X4,X0,X6,X2),c_Pair(X5,X1,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2)),c_Wellfounded_Olex__prod(X7,X3,X6,X2),tc_prod(tc_prod(X6,X2),tc_prod(X6,X2)))
      | c_in(c_Pair(X4,X5,X6,X6),X7,tc_prod(X6,X6))
      | c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_1) ).

fof(f407,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),X6,tc_prod(X2,X2))
      | c_in(c_Pair(c_Pair(X0,X1,X2,X3),c_Pair(X4,X5,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X6,X7,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_2) ).

fof(f408,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(X1,X4,X3,X3),X6,tc_prod(X3,X3))
      | c_in(c_Pair(c_Pair(X0,X1,X2,X3),c_Pair(X0,X4,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_3) ).

fof(f409,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,X2,X5),c_Pair(X1,X6,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5)),c_Wellfounded_Olex__prod(X3,X7,X2,X5),tc_prod(tc_prod(X2,X5),tc_prod(X2,X5)))
      | c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_0) ).

fof(f410,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed1_0) ).

fof(f411,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

fof(f412,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X0,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

fof(f413,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X3,X1,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

fof(f414,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

fof(f415,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

fof(f416,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X5,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

fof(f417,axiom,
    ! [X2,X0,X1] : c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

fof(f418,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X0,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

fof(f419,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X5,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X7),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

fof(f420,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

fof(f421,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X4,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X3),X1,X4,X5)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X1,X3)
      | c_TypeSafe__Mirabelle_Osconf(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__preserves__sconf_0) ).

fof(f422,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp1Reds_0) ).

fof(f423,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X0,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssReds_0) ).

fof(f424,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X5,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryReds_0) ).

fof(f425,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowRedsThrow_0) ).

fof(f426,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X0,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastReds_0) ).

fof(f427,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsObj_0) ).

fof(f428,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X3,X1,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds_0) ).

fof(f429,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondReds_0) ).

fof(f430,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowReds_0) ).

fof(f431,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X4,X1,X2,tc_List_Olist(tc_String_Ochar)),X5,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccReds_0) ).

fof(f432,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X0,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X5,X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X6,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X7),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds1_0) ).

fof(f433,axiom,
    ! [X2,X0,X1] :
      ( ~ c_List_Olist__all2(c_fequal(X2),X0,X1,X2,X2)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

fof(f434,axiom,
    ! [X0,X1] : c_COMBI(X0,X1) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

fof(f435,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X1,X0,X2)
      | hBOOL(hAPP(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f436,axiom,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(X1,X0))
      | c_in(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f437,axiom,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ c_in(c_Pair(c_Pair(X4,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X3),X1,X4,X5)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X1,X3)
      | c_TypeSafe__Mirabelle_Osconf(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__preserves__sconf_0) ).

fof(f438,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_TypeSafe__Mirabelle_Osconf(X0,X1,X2)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X1,X3,X4)
      | c_TypeSafe__Mirabelle_Owf__config(X0,X1,X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__config__def_2) ).

fof(f439,axiom,
    ! [X2,X0,X1] :
      ( ~ c_in(X0,X1,tc_prod(X2,X2))
      | c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

fof(f441,axiom,
    ! [X2,X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

fof(f442,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

fof(f443,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

fof(f444,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

fof(f445,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( X0 = X4
      | c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

fof(f446,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( X1 = X5
      | c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

fof(f447,axiom,
    ! [X0,X1] : c_List_Olist__all2(c_fequal(X0),X1,X1,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).

fof(f448,axiom,
    ! [X0,X1] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

fof(f449,plain,
    ! [X0,X1] : c_Transitive__Closure_Ortrancl(X0,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),
    inference(reorient_equations,[],[f448]) ).

fof(f450,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_TypeSafe__Mirabelle_Owf__config(X0,X1,X2,X3,X4)
      | c_TypeSafe__Mirabelle_Osconf(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__config__def_0) ).

fof(f452,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_TypeSafe__Mirabelle_Owf__config(X0,X2,X1,X3,X4)
      | c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__config__def_1) ).

fof(f453,axiom,
    ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).

fof(f454,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X4))
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X4),X3))
      | hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__trans_0) ).

fof(f455,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X1,X2),X3),X5))
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X2),X5),X4))
      | hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X1,X2),X3),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__widen_0) ).

fof(f458,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X2,X4,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X4,X3,tc_Type_Oty,tc_Type_Oty)
      | c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X2,X3,tc_Type_Oty,tc_Type_Oty) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__trans_0) ).

fof(f459,axiom,
    ! [X2,X0,X1] : c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X2,X2,tc_Type_Oty,tc_Type_Oty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__refl_0) ).

fof(f460,axiom,
    c_in(c_Pair(c_Pair(v_e,v_s,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(v_e_H,v_s_H,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

fof(f461,negated_conjecture,
    c_TypeSafe__Mirabelle_Owf__config(v_P,v_E,v_s,v_e,v_T),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f462,negated_conjecture,
    ! [X0] :
      ( ~ c_TypeSafe__Mirabelle_Owf__config(v_P,v_E,v_s_H,v_e_H,X0)
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X0),v_T)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f463,axiom,
    ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f464,axiom,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal(X2),X0),X1))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f466,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X2),X2,X3),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2)) ),
    inference(definition_unfolding,[],[f126,f166]) ).

fof(f467,plain,
    ! [X2,X3,X0,X1] :
      ( ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X2),X2,X3),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X3),X0,X3,X2),X1,tc_prod(X3,X2)) ),
    inference(definition_unfolding,[],[f127,f166]) ).

fof(f472,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(definition_unfolding,[],[f361,f166]) ).

tcf(c_462,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ( c_Value_Oval_OAddr(X0) != c_Value_Oval_OAddr(X1) ) ),
    inference(cnf_transformation,[],[f1]) ).

tcf(c_465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f4]) ).

tcf(c_466,plain,
    ! [X0: $i] : c_Value_Oval_OAddr(X0) != c_Value_Oval_OUnit,
    inference(cnf_transformation,[],[f6]) ).

tcf(c_467,plain,
    ! [X0: $i] : c_Value_Oval_OAddr(X0) != c_Value_Oval_ONull,
    inference(cnf_transformation,[],[f8]) ).

tcf(c_468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f9]) ).

tcf(c_472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f13]) ).

tcf(c_476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OBlock(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f17]) ).

tcf(c_478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f20]) ).

tcf(c_482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    inference(cnf_transformation,[],[f24]) ).

tcf(c_484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    inference(cnf_transformation,[],[f28]) ).

tcf(c_485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f29]) ).

tcf(c_486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_489,plain,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    inference(cnf_transformation,[],[f36]) ).

tcf(c_490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    inference(cnf_transformation,[],[f38]) ).

tcf(c_491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f40]) ).

tcf(c_492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    inference(cnf_transformation,[],[f41]) ).

tcf(c_493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    inference(cnf_transformation,[],[f43]) ).

tcf(c_494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2 = X6 )
      | ( c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f45]) ).

tcf(c_495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ( c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f47]) ).

tcf(c_496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X4 )
      | ( c_Expr_Oexp_OBlock(X0,X1,X2,X3) != c_Expr_Oexp_OBlock(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OBlock(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f50]) ).

tcf(c_498,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f51]) ).

tcf(c_499,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ( c_Expr_Oexp_OVal(X0,X1) != c_Expr_Oexp_OVal(X2,X1) ) ),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_511,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),c_Wellfounded_Oacc(X0,X2),X2) ),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    inference(cnf_transformation,[],[f67]) ).

tcf(c_516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OVal(X5,X4),
    inference(cnf_transformation,[],[f69]) ).

tcf(c_517,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1))) ),
    inference(cnf_transformation,[],[f70]) ).

tcf(c_518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    inference(cnf_transformation,[],[f72]) ).

tcf(c_521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_Othrow(X3,X2),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    inference(cnf_transformation,[],[f78]) ).

tcf(c_526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OWhile(X5,X6,X4),
    inference(cnf_transformation,[],[f80]) ).

tcf(c_527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    inference(cnf_transformation,[],[f82]) ).

tcf(c_531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OVal(X5,X4),
    inference(cnf_transformation,[],[f87]) ).

tcf(c_532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    inference(cnf_transformation,[],[f91]) ).

tcf(c_535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2),
    inference(cnf_transformation,[],[f92]) ).

tcf(c_536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f93]) ).

tcf(c_537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f94]) ).

tcf(c_538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_WellTypeRT_OWTrt(X0,X5,X2,X3,X4)
      | ~ c_Objects_Ohext(X1,X5)
      | ~ c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_539,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Objects_Ohext(X0,X2)
      | ~ c_Objects_Ohext(X1,X2)
      | ~ c_Objects_Ohext(X0,X1) ),
    inference(cnf_transformation,[],[f96]) ).

tcf(c_541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_List_Olist__all2(c_Conform_Oconf(X0,X5,X2),X3,X4,tc_Value_Oval,tc_Type_Oty)
      | ~ c_Objects_Ohext(X1,X5)
      | ~ c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X4,tc_Value_Oval,tc_Type_Oty) ),
    inference(cnf_transformation,[],[f98]) ).

tcf(c_542,plain,
    ! [X0: $i] : c_Objects_Ohext(X0,X0),
    inference(cnf_transformation,[],[f99]) ).

tcf(c_543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X5,X2),X3),X4))
      | ~ c_Objects_Ohext(X1,X5)
      | ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X1,X2),X3),X4)) ),
    inference(cnf_transformation,[],[f100]) ).

tcf(c_544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    inference(cnf_transformation,[],[f101]) ).

tcf(c_545,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Wellfounded_Oacc(X0,X2),X2) ),
    inference(cnf_transformation,[],[f102]) ).

tcf(c_546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OWhile(X4,X5,X3),
    inference(cnf_transformation,[],[f104]) ).

tcf(c_547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OVal(X4,X3),
    inference(cnf_transformation,[],[f106]) ).

tcf(c_548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X3 )
      | ( c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f107]) ).

tcf(c_549,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ( c_Expr_Oexp_OWhile(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f108]) ).

tcf(c_550,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(cnf_transformation,[],[f109]) ).

tcf(c_551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2),
    inference(cnf_transformation,[],[f110]) ).

tcf(c_552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OVal(X3,X2),
    inference(cnf_transformation,[],[f111]) ).

tcf(c_553,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1))) ),
    inference(cnf_transformation,[],[f112]) ).

tcf(c_554,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_Expr_Oexp_OVal(X0,X1) != c_Expr_Oexp_Othrow(X2,X1),
    inference(cnf_transformation,[],[f113]) ).

tcf(c_555,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OWhile(X5,X6,X4),
    inference(cnf_transformation,[],[f114]) ).

tcf(c_556,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OWhile(X3,X4,X2),
    inference(cnf_transformation,[],[f115]) ).

tcf(c_557,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f116]) ).

tcf(c_558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X4,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f117]) ).

tcf(c_559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),c_Expr_Oexp_OVal(X3,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f118]) ).

tcf(c_560,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(X0,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(cnf_transformation,[],[f119]) ).

tcf(c_561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(cnf_transformation,[],[f120]) ).

tcf(c_562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(X0,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(cnf_transformation,[],[f121]) ).

tcf(c_563,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f122]) ).

tcf(c_564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(cnf_transformation,[],[f123]) ).

tcf(c_565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(cnf_transformation,[],[f124]) ).

tcf(c_566,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2),X0,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f125]) ).

tcf(c_567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),X0,X2,X3),X1,tc_prod(X2,X3))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(cnf_transformation,[],[f466]) ).

tcf(c_568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),X0,X2,X3),X1,tc_prod(X2,X3))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(cnf_transformation,[],[f467]) ).

tcf(c_569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_List_Olist__all2(c_TypeRel_Owiden(X0,X2),c_Conform_Osko__Conform__Xconfs__conv__map__1__1(X0,X4,X1,X3,X2),X4,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X4,tc_Value_Oval,tc_Type_Oty) ),
    inference(cnf_transformation,[],[f128]) ).

tcf(c_570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_Objects_Ohext(X1,X4)
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f129]) ).

tcf(c_571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f130]) ).

tcf(c_572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X7,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X7,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f131]) ).

tcf(c_573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f132]) ).

tcf(c_574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f133]) ).

tcf(c_575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f134]) ).

tcf(c_578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f137]) ).

tcf(c_579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f138]) ).

tcf(c_580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f139]) ).

tcf(c_581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X7,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,tc_List_Olist(tc_String_Ochar)),X6,X7,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f140]) ).

tcf(c_582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X5,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f141]) ).

tcf(c_583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f142]) ).

tcf(c_584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X8,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,tc_List_Olist(tc_String_Ochar)),X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X5,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,tc_List_Olist(tc_String_Ochar)),X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f143]) ).

tcf(c_585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X8,X9,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,tc_List_Olist(tc_String_Ochar)),X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X5,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,tc_List_Olist(tc_String_Ochar)),X7,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f144]) ).

tcf(c_586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Owf__config(X4,X5,X3,X2,v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X5,X4,X6,X2,X3))
      | ~ c_TypeSafe__Mirabelle_Owf__config(X4,X5,X1,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f145]) ).

tcf(c_587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X5,X4,X6,X2,X3)),X6))
      | ~ c_TypeSafe__Mirabelle_Owf__config(X4,X5,X1,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f146]) ).

tcf(c_588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_WellTypeRT_OWTrt(X6,X4,X7,X3,v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X7,X6,X8,X3,X4))
      | ~ c_WellTypeRT_OWTrt(X6,X1,X7,X0,X8)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X6,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X6,X7,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f147]) ).

tcf(c_589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X6,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X7,X6,X8,X3,X4)),X8))
      | ~ c_WellTypeRT_OWTrt(X6,X1,X7,X0,X8)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X6,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X6,X7,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f148]) ).

tcf(c_590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OSeq(X3,X5,tc_List_Olist(tc_String_Ochar)),X6)
      | ~ c_WellTypeRT_OWTrt(X0,X1,X2,X5,X6)
      | ~ c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f149]) ).

tcf(c_591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ( c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OLAss(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f150]) ).

tcf(c_592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X3 )
      | ( c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OLAss(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f151]) ).

tcf(c_596,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),
    inference(cnf_transformation,[],[f155]) ).

tcf(c_603,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f163]) ).

tcf(c_609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2 = X6 )
      | ( c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f173]) ).

tcf(c_610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ( c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f174]) ).

tcf(c_611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X4 )
      | ( c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f175]) ).

tcf(c_613,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X3 = X8 )
      | ( c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f177]) ).

tcf(c_614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X2 = X7 )
      | ( c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f178]) ).

tcf(c_615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X6 )
      | ( c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f179]) ).

tcf(c_616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X0 = X5 )
      | ( c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f180]) ).

tcf(c_617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    inference(cnf_transformation,[],[f181]) ).

tcf(c_618,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2 = X6 )
      | ( c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f183]) ).

tcf(c_619,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ( c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f185]) ).

tcf(c_620,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X4 )
      | ( c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f187]) ).

tcf(c_622,plain,
    c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),
    inference(cnf_transformation,[],[f189]) ).

tcf(c_626,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    inference(cnf_transformation,[],[f194]) ).

tcf(c_629,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OSeq(X5,X6,X4),
    inference(cnf_transformation,[],[f197]) ).

tcf(c_631,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f199]) ).

tcf(c_632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f200]) ).

tcf(c_633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f201]) ).

tcf(c_634,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f202]) ).

tcf(c_635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f203]) ).

tcf(c_637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f205]) ).

tcf(c_638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f206]) ).

tcf(c_639,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f207]) ).

tcf(c_641,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X0,X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f209]) ).

tcf(c_642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(X4,X2,X3)
      | ~ c_in(c_Pair(X0,X5,X2,X3),X4,tc_prod(X2,X3))
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f210]) ).

tcf(c_643,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f211]) ).

tcf(c_644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f212]) ).

tcf(c_645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f213]) ).

tcf(c_646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f214]) ).

tcf(c_647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f215]) ).

tcf(c_648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f216]) ).

tcf(c_649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,X3,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f217]) ).

tcf(c_650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,tc_List_Olist(tc_String_Ochar)),X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f218]) ).

tcf(c_651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f219]) ).

tcf(c_652,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X4,c_State_Ohp(X3),X5,X2,v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X5,X4,X6,X2,X3))
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f220]) ).

tcf(c_653,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f221]) ).

tcf(c_654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f222]) ).

tcf(c_655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f223]) ).

tcf(c_656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f224]) ).

tcf(c_657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f225]) ).

tcf(c_661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAcc(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f229]) ).

tcf(c_662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    inference(cnf_transformation,[],[f231]) ).

tcf(c_670,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1) = X0,
    inference(cnf_transformation,[],[f241]) ).

tcf(c_675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Map_Omap__add(c_Map_Omap__add(X0,X1,X2,X3),X4,X2,X3) = c_Map_Omap__add(X0,c_Map_Omap__add(X1,X4,X2,X3),X2,X3),
    inference(cnf_transformation,[],[f247]) ).

tcf(c_676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X0 = X5 )
      | ( c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f248]) ).

tcf(c_677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X6 )
      | ( c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f249]) ).

tcf(c_678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X2 = X7 )
      | ( c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f250]) ).

tcf(c_679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X3 = X8 )
      | ( c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAss(X5,X6,X7,X8,X4) ) ),
    inference(cnf_transformation,[],[f251]) ).

tcf(c_680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X4 )
      | ( c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f252]) ).

tcf(c_681,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ( c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f253]) ).

tcf(c_682,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2 = X6 )
      | ( c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OFAcc(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f254]) ).

tcf(c_683,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    inference(cnf_transformation,[],[f255]) ).

tcf(c_684,plain,
    ! [X0: $i,X1: $i] : c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1) = c_Relation_OId__on(X0,X1),
    inference(cnf_transformation,[],[f257]) ).

tcf(c_685,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    inference(cnf_transformation,[],[f259]) ).

tcf(c_687,plain,
    ! [X0: $i,X1: $i] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),
    inference(cnf_transformation,[],[f261]) ).

tcf(c_690,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f266]) ).

tcf(c_691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_Othrow(X3,X2),
    inference(cnf_transformation,[],[f267]) ).

tcf(c_692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    inference(cnf_transformation,[],[f269]) ).

tcf(c_693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2),
    inference(cnf_transformation,[],[f270]) ).

tcf(c_695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f274]) ).

tcf(c_698,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    inference(cnf_transformation,[],[f278]) ).

tcf(c_699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    inference(cnf_transformation,[],[f279]) ).

tcf(c_700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OTryCatch(X5,X6,X7,X8,X4),
    inference(cnf_transformation,[],[f280]) ).

tcf(c_702,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ( c_Expr_Oexp_Othrow(X0,X1) != c_Expr_Oexp_Othrow(X2,X1) ) ),
    inference(cnf_transformation,[],[f283]) ).

tcf(c_703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OSeq(X4,X5,X3),
    inference(cnf_transformation,[],[f284]) ).

tcf(c_705,plain,
    ! [X0: $i,X1: $i] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X1),X1),
    inference(cnf_transformation,[],[f286]) ).

tcf(c_708,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCast(X5,X6,X4),
    inference(cnf_transformation,[],[f289]) ).

tcf(c_709,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCast(X5,X6,X4),
    inference(cnf_transformation,[],[f290]) ).

tcf(c_710,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCond(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    inference(cnf_transformation,[],[f292]) ).

tcf(c_711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OLAss(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2),
    inference(cnf_transformation,[],[f293]) ).

tcf(c_712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCall(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f294]) ).

tcf(c_713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f296]) ).

tcf(c_714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OFAcc(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f297]) ).

tcf(c_716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_Othrow(X3,X2),
    inference(cnf_transformation,[],[f300]) ).

tcf(c_717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OLAss(X5,X6,X4),
    inference(cnf_transformation,[],[f301]) ).

tcf(c_718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    inference(cnf_transformation,[],[f302]) ).

tcf(c_719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    inference(cnf_transformation,[],[f303]) ).

tcf(c_720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OBinOp(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f304]) ).

tcf(c_723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    inference(cnf_transformation,[],[f307]) ).

tcf(c_724,plain,
    ! [X0: $i,X1: $i] : c_Relation_ODomain(c_Relation_OId__on(X0,X1),X1,X1) = X0,
    inference(cnf_transformation,[],[f308]) ).

tcf(c_725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_Othrow(X5,X4),
    inference(cnf_transformation,[],[f309]) ).

tcf(c_726,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X4 )
      | ( c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f311]) ).

tcf(c_727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ( c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f313]) ).

tcf(c_728,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2 = X6 )
      | ( c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3) ) ),
    inference(cnf_transformation,[],[f315]) ).

tcf(c_729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCond(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f316]) ).

tcf(c_731,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(cnf_transformation,[],[f318]) ).

tcf(c_732,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(cnf_transformation,[],[f319]) ).

tcf(c_733,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_Othrow(X3,X2),
    inference(cnf_transformation,[],[f320]) ).

tcf(c_734,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    inference(cnf_transformation,[],[f321]) ).

tcf(c_736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OCond(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f323]) ).

tcf(c_737,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    inference(cnf_transformation,[],[f324]) ).

tcf(c_738,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X3 )
      | ( c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f325]) ).

tcf(c_739,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ( c_Expr_Oexp_OCast(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f326]) ).

tcf(c_740,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCond(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f327]) ).

tcf(c_741,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OCall(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f329]) ).

tcf(c_742,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_Othrow(X5,X4),
    inference(cnf_transformation,[],[f330]) ).

tcf(c_743,plain,
    ! [X0: $i,X1: $i] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1) = c_Relation_ODomain(X0,X1,X1),
    inference(cnf_transformation,[],[f331]) ).

tcf(c_744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OBinOp(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f332]) ).

tcf(c_745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OBinOp(X0,X1,X2,X3) != c_Expr_Oexp_OLAss(X4,X5,X3),
    inference(cnf_transformation,[],[f333]) ).

tcf(c_746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X3 )
      | ( c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f334]) ).

tcf(c_747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ( c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OSeq(X3,X4,X2) ) ),
    inference(cnf_transformation,[],[f335]) ).

tcf(c_748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Expr_Oexp_OCall(X0,X1,X2,X3) != c_Expr_Oexp_OCast(X4,X5,X3),
    inference(cnf_transformation,[],[f337]) ).

tcf(c_749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OSeq(X5,X6,X4),
    inference(cnf_transformation,[],[f338]) ).

tcf(c_750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_Expr_Oexp_OFAss(X0,X1,X2,X3,X4) != c_Expr_Oexp_OBinOp(X5,X6,X7,X4),
    inference(cnf_transformation,[],[f339]) ).

tcf(c_751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OTryCatch(X0,X1,X2,X3,X4) != c_Expr_Oexp_OLAss(X5,X6,X4),
    inference(cnf_transformation,[],[f340]) ).

tcf(c_752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_OCall(X4,X5,X6,X3),
    inference(cnf_transformation,[],[f342]) ).

tcf(c_753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OFAcc(X0,X1,X2,X3) != c_Expr_Oexp_Othrow(X4,X3),
    inference(cnf_transformation,[],[f343]) ).

tcf(c_754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_Expr_Oexp_OSeq(X0,X1,X2) != c_Expr_Oexp_OCast(X3,X4,X2),
    inference(cnf_transformation,[],[f344]) ).

tcf(c_755,plain,
    ! [X0: $i,X1: $i] : c_Relation_Osingle__valued(c_Relation_OId__on(X0,X1),X1,X1),
    inference(cnf_transformation,[],[f345]) ).

tcf(c_756,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f346]) ).

tcf(c_757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,tc_List_Olist(tc_String_Ochar),tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f347]) ).

tcf(c_758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f348]) ).

tcf(c_759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f349]) ).

tcf(c_761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ~ c_Relation_Orefl__on(X4,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f351]) ).

tcf(c_762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ~ c_Relation_Orefl__on(X4,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f352]) ).

tcf(c_763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X1,X3,X2)
      | ~ c_in(X0,X1,X2) ),
    inference(cnf_transformation,[],[f353]) ).

tcf(c_765,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f356]) ).

tcf(c_766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,hAPP(X5,X0),X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f357]) ).

tcf(c_768,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f359]) ).

tcf(c_770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X4,X2,X3),X3,X2),X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f472]) ).

tcf(c_771,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,X1,X2) ),
    inference(cnf_transformation,[],[f364]) ).

tcf(c_772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f365]) ).

tcf(c_774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
      | ~ c_in(X0,X5,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(cnf_transformation,[],[f367]) ).

tcf(c_776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f369]) ).

tcf(c_778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X2,X0,X5,X3),c_Product__Type_OSigma(X4,X1,X5,X3),tc_prod(X5,X3))
      | ~ c_in(X2,X4,X5)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(cnf_transformation,[],[f371]) ).

tcf(c_779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X4,c_State_Ohp(X3),X5,X2,v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X5,X4,X6,X2,X3))
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f372]) ).

tcf(c_780,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X5,X4,X6,X2,X3)),X6))
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f373]) ).

tcf(c_781,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f374]) ).

tcf(c_782,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f375]) ).

tcf(c_783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f376]) ).

tcf(c_784,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f377]) ).

tcf(c_785,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(cnf_transformation,[],[f379]) ).

tcf(c_786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2)))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f380]) ).

tcf(c_789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f383]) ).

tcf(c_790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f384]) ).

tcf(c_791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f385]) ).

tcf(c_792,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(cnf_transformation,[],[f387]) ).

tcf(c_793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f388]) ).

tcf(c_794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f389]) ).

tcf(c_795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f390]) ).

tcf(c_796,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f391]) ).

tcf(c_797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f392]) ).

tcf(c_798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f393]) ).

tcf(c_799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f394]) ).

tcf(c_800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2)))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f395]) ).

tcf(c_801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f396]) ).

tcf(c_802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f397]) ).

tcf(c_803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f398]) ).

tcf(c_804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X5,X4,X6,X2,X3)),X6))
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f399]) ).

tcf(c_805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X5,tc_Value_Oval,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X2),X4,X5,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X4,tc_Value_Oval,tc_Type_Oty) ),
    inference(cnf_transformation,[],[f400]) ).

tcf(c_806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f401]) ).

tcf(c_809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f404]) ).

tcf(c_810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X4,X0,X6,X2),c_Pair(X4,X1,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2)),c_Recdef_Osame__fst(X5,X3,X6,X2),tc_prod(tc_prod(X6,X2),tc_prod(X6,X2)))
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f405]) ).

tcf(c_811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X5,X3,X3),X7,tc_prod(X3,X3))
      | c_in(c_Pair(X0,X4,X2,X2),X6,tc_prod(X2,X2))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),c_Pair(X4,X5,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X6,X7,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(cnf_transformation,[],[f406]) ).

tcf(c_812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,X4,X2,X5),c_Pair(X1,X6,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5)),c_Wellfounded_Olex__prod(X3,X7,X2,X5),tc_prod(tc_prod(X2,X5),tc_prod(X2,X5)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f407]) ).

tcf(c_813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X4,X0,X5,X2),c_Pair(X4,X1,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2)),c_Wellfounded_Olex__prod(X6,X3,X5,X2),tc_prod(tc_prod(X5,X2),tc_prod(X5,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f408]) ).

tcf(c_814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),X6,tc_prod(X2,X2))
      | ( X0 = X4 )
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),c_Pair(X4,X5,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X6,X7,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(cnf_transformation,[],[f409]) ).

tcf(c_815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f410]) ).

tcf(c_816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f411]) ).

tcf(c_817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f412]) ).

tcf(c_818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f413]) ).

tcf(c_819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f414]) ).

tcf(c_820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f415]) ).

tcf(c_821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f416]) ).

tcf(c_822,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f417]) ).

tcf(c_823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f418]) ).

tcf(c_824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f419]) ).

tcf(c_825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f420]) ).

tcf(c_826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_WellForm_Owf__prog(c_JWellForm_Owf__J__mdecl,X4,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f421]) ).

tcf(c_827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f422]) ).

tcf(c_828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f423]) ).

tcf(c_829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f424]) ).

tcf(c_830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f425]) ).

tcf(c_831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f426]) ).

tcf(c_832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f427]) ).

tcf(c_833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f428]) ).

tcf(c_834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f429]) ).

tcf(c_835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f430]) ).

tcf(c_836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f431]) ).

tcf(c_837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,tc_List_Olist(tc_String_Ochar)),X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f432]) ).

tcf(c_838,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ c_List_Olist__all2(c_fequal(X0),X1,X2,X0,X0) ),
    inference(cnf_transformation,[],[f433]) ).

tcf(c_839,plain,
    ! [X0: $i,X1: $i] : c_COMBI(X0,X1) = X0,
    inference(cnf_transformation,[],[f434]) ).

tcf(c_840,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X1,X0))
      | ~ c_in(X0,X1,X2) ),
    inference(cnf_transformation,[],[f435]) ).

tcf(c_841,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,X0,X2)
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(cnf_transformation,[],[f436]) ).

tcf(c_842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(cnf_transformation,[],[f437]) ).

tcf(c_843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_TypeSafe__Mirabelle_Owf__config(X0,X2,X1,X3,X4)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X2,X1)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,X4) ),
    inference(cnf_transformation,[],[f438]) ).

tcf(c_844,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f439]) ).

tcf(c_846,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1)),
    inference(cnf_transformation,[],[f441]) ).

tcf(c_847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f442]) ).

tcf(c_848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f443]) ).

tcf(c_849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(cnf_transformation,[],[f444]) ).

tcf(c_850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X0 = X4 )
      | ( c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ) ),
    inference(cnf_transformation,[],[f445]) ).

tcf(c_851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X1 = X5 )
      | ( c_Pair(X0,X1,X2,X3) != c_Pair(X4,X5,X2,X3) ) ),
    inference(cnf_transformation,[],[f446]) ).

tcf(c_852,plain,
    ! [X0: $i,X1: $i] : c_List_Olist__all2(c_fequal(X0),X1,X1,X0,X0),
    inference(cnf_transformation,[],[f447]) ).

tcf(c_853,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    inference(cnf_transformation,[],[f449]) ).

tcf(c_854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X0,X1,X2)
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f450]) ).

tcf(c_856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X1,X3,X4)
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f452]) ).

tcf(c_857,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X2)),
    inference(cnf_transformation,[],[f453]) ).

tcf(c_858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X4))
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X3),X4))
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3)) ),
    inference(cnf_transformation,[],[f454]) ).

tcf(c_859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X1,X2),X3),X5))
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,X2),X4),X5))
      | ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(X0,X1,X2),X3),X4)) ),
    inference(cnf_transformation,[],[f455]) ).

tcf(c_861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X2,X4,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X3,X4,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X2,X3,tc_Type_Oty,tc_Type_Oty) ),
    inference(cnf_transformation,[],[f458]) ).

tcf(c_862,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_List_Olist__all2(c_TypeRel_Owiden(X0,X1),X2,X2,tc_Type_Oty,tc_Type_Oty),
    inference(cnf_transformation,[],[f459]) ).

tcf(c_863,plain,
    c_in(c_Pair(c_Pair(v_e,v_s,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(v_e_H,v_s_H,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))),
    inference(cnf_transformation,[],[f460]) ).

tcf(c_864,negated_conjecture,
    c_TypeSafe__Mirabelle_Owf__config(v_P,v_E,v_s,v_e,v_T),
    inference(cnf_transformation,[],[f461]) ).

tcf(c_865,negated_conjecture,
    ! [X0: $i] :
      ( ~ c_TypeSafe__Mirabelle_Owf__config(v_P,v_E,v_s_H,v_e_H,X0)
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X0),v_T)) ),
    inference(cnf_transformation,[],[f462]) ).

tcf(c_866,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)),
    inference(cnf_transformation,[],[f463]) ).

tcf(c_867,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2)) ),
    inference(cnf_transformation,[],[f464]) ).

tcf(c_4196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X7,X0,X8,X4,X5)),X8))
      | ~ c_WellTypeRT_OWTrt(X0,X2,X7,X1,X8)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X7,c_Pair(X2,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_in(c_Pair(c_Pair(X1,c_Pair(X2,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X5,X6,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_589,c_622]) ).

tcf(c_4197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X6,v_P,X7,X3,X4)),X7))
      | ~ c_WellTypeRT_OWTrt(v_P,X1,X6,X0,X7)
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X6,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(v_P),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4196]) ).

tcf(c_4211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_WellTypeRT_OWTrt(X0,X5,X7,X4,v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X7,X0,X8,X4,X5))
      | ~ c_WellTypeRT_OWTrt(X0,X2,X7,X1,X8)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X7,c_Pair(X2,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_in(c_Pair(c_Pair(X1,c_Pair(X2,X3,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X4,c_Pair(X5,X6,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_588,c_622]) ).

tcf(c_4212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_WellTypeRT_OWTrt(v_P,X4,X6,X3,v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1(X6,v_P,X7,X3,X4))
      | ~ c_WellTypeRT_OWTrt(v_P,X1,X6,X0,X7)
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X6,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(v_P),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4211]) ).

tcf(c_4226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X0,X5,X4)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X5,X2)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X5,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_826,c_622]) ).

tcf(c_4227,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(v_P,X4,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X4,X1)
      | ~ c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X1),X4,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4226]) ).

tcf(c_4240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X5,X0,X6,X3,X4)),X6))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X5,X2)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X5,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_804,c_622]) ).

tcf(c_4241,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X4,v_P,X5,X2,X3)),X5))
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X4,X1)
      | ~ c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X1),X4,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4240]) ).

tcf(c_4255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X5,X0,X6,X3,X4)),X6))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X5,X2)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X5,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_780,c_622]) ).

tcf(c_4256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X4,v_P,X5,X2,X3)),X5))
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X4,X1)
      | ~ c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X1),X4,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(v_P),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4255]) ).

tcf(c_4270,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X0,c_State_Ohp(X4),X5,X3,v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X5,X0,X6,X3,X4))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X5,X2)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X5,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_779,c_622]) ).

tcf(c_4271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X3),X4,X2,v_sko__TypeSafe__Mirabelle__XRed__preserves__type__1(X4,v_P,X5,X2,X3))
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X4,X1)
      | ~ c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X1),X4,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4270]) ).

tcf(c_4285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X0,c_State_Ohp(X4),X5,X3,v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X5,X0,X6,X3,X4))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X5,X2)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X2),X5,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_652,c_622]) ).

tcf(c_4286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X3),X4,X2,v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1(X4,v_P,X5,X2,X3))
      | ~ c_TypeSafe__Mirabelle_Osconf(v_P,X4,X1)
      | ~ c_WellTypeRT_OWTrt(v_P,c_State_Ohp(X1),X4,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(v_P),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4285]) ).

tcf(c_4300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X0,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X5,X0,X6,X3,X4)),X6))
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X5,X2,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_587,c_622]) ).

tcf(c_4301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X4,v_P,X5,X2,X3)),X5))
      | ~ c_TypeSafe__Mirabelle_Owf__config(v_P,X4,X1,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(v_P),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4300]) ).

tcf(c_4312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Owf__config(X0,X5,X4,X3,v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X5,X0,X6,X3,X4))
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X5,X2,X1,X6)
      | ~ c_in(c_Pair(c_Pair(X1,X2,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X0),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))))
      | ( c_JWellForm_Owf__J__mdecl != c_JWellForm_Owf__J__mdecl )
      | ( X0 != v_P )
      | ( tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) != tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))) ) ),
    inference(resolution_lifted,[status(thm)],[c_586,c_622]) ).

tcf(c_4313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_TypeSafe__Mirabelle_Owf__config(v_P,X4,X3,X2,v_sko__TypeSafe__Mirabelle__XSubject__reduction__1(X4,v_P,X5,X2,X3))
      | ~ c_TypeSafe__Mirabelle_Owf__config(v_P,X4,X1,X0,X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(v_P),tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)),tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(unflattening,[status(thm)],[c_4312]) ).

tcf(c_7263,definition,
    iPr_def_10 = tc_List_Olist(tc_String_Ochar),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_7264,definition,
    iPr_def_11 = tc_List_Olist(iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_7265,definition,
    iPr_def_12 = tc_Expr_Oexp(iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_7266,definition,
    iPr_def_13 = tc_prod(iPr_def_11,iPr_def_12),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_7267,definition,
    iPr_def_14 = c_TypeRel_Owiden(v_P,iPr_def_13),
    introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).

tcf(c_7268,negated_conjecture,
    ! [X0: $i] :
      ( ~ c_TypeSafe__Mirabelle_Owf__config(v_P,v_E,v_s_H,v_e_H,X0)
      | ~ hBOOL(hAPP(hAPP(iPr_def_14,X0),v_T)) ),
    inference(demodulation,[status(thm)],[c_865,c_7265,c_7263,c_7264,c_7266,c_7267]) ).

tcf(c_7269,negated_conjecture,
    c_TypeSafe__Mirabelle_Owf__config(v_P,v_E,v_s,v_e,v_T),
    inference(demodulation,[status(thm)],[c_864]) ).

tcf(c_16694,plain,
    ! [X0: $i] : hBOOL(hAPP(hAPP(iPr_def_14,X0),X0)),
    inference(superposition,[status(thm)],[c_7267,c_857]) ).

tcf(c_16718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),
    inference(superposition,[status(thm)],[c_857,c_841]) ).

tcf(c_16720,plain,
    ! [X0: $i,X1: $i] : c_in(X0,hAPP(iPr_def_14,X0),X1),
    inference(superposition,[status(thm)],[c_16694,c_841]) ).

tcf(c_16765,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(X2,X2,X1,X1))),
    inference(superposition,[status(thm)],[c_846,c_840]) ).

tcf(c_16768,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),X3),
    inference(superposition,[status(thm)],[c_16765,c_841]) ).

tcf(c_17001,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_840]) ).

tcf(c_17011,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X0)),
    inference(superposition,[status(thm)],[c_16720,c_17001]) ).

tcf(c_17012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),c_Pair(X3,X3,X1,X1))),
    inference(superposition,[status(thm)],[c_16768,c_17001]) ).

tcf(c_17045,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),
    inference(superposition,[status(thm)],[c_17011,c_841]) ).

tcf(c_17252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),
    inference(superposition,[status(thm)],[c_17012,c_841]) ).

tcf(c_17308,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_17252,c_17001]) ).

tcf(c_17363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_17308,c_841]) ).

tcf(c_17633,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_840]) ).

tcf(c_17784,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X0)),
    inference(superposition,[status(thm)],[c_16720,c_17633]) ).

tcf(c_17785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),c_Pair(X3,X3,X1,X1))),
    inference(superposition,[status(thm)],[c_16768,c_17633]) ).

tcf(c_17791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_17252,c_17633]) ).

tcf(c_18143,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),
    inference(superposition,[status(thm)],[c_17784,c_841]) ).

tcf(c_18887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),
    inference(superposition,[status(thm)],[c_17785,c_841]) ).

tcf(c_19225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_18887,c_17633]) ).

tcf(c_19226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_18887,c_17001]) ).

tcf(c_19695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_17791,c_841]) ).

tcf(c_20895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_19225,c_841]) ).

tcf(c_20900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_19226,c_841]) ).

tcf(c_21873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X4,X5),X4),
    inference(superposition,[status(thm)],[c_16718,c_768]) ).

tcf(c_21876,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_16768,c_768]) ).

tcf(c_21877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X2),
    inference(superposition,[status(thm)],[c_17045,c_768]) ).

tcf(c_21882,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),
    inference(superposition,[status(thm)],[c_17252,c_768]) ).

tcf(c_21886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_17363,c_768]) ).

tcf(c_21889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X2),
    inference(superposition,[status(thm)],[c_18143,c_768]) ).

tcf(c_21898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),
    inference(superposition,[status(thm)],[c_18887,c_768]) ).

tcf(c_21910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_19695,c_768]) ).

tcf(c_22807,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_21876,c_840]) ).

tcf(c_22938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_22807,c_841]) ).

tcf(c_22941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_22938,c_17633]) ).

tcf(c_22942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_22938,c_17001]) ).

tcf(c_22943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X3),
    inference(superposition,[status(thm)],[c_22938,c_768]) ).

tcf(c_22952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_21882,c_840]) ).

tcf(c_23188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_21898,c_840]) ).

tcf(c_23193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_22941,c_841]) ).

tcf(c_23198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_22942,c_841]) ).

tcf(c_23297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),
    inference(superposition,[status(thm)],[c_22952,c_841]) ).

tcf(c_23303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),
    inference(superposition,[status(thm)],[c_23188,c_841]) ).

tcf(c_23306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_23193,c_17633]) ).

tcf(c_23307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_23193,c_17001]) ).

tcf(c_23334,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_23198,c_17633]) ).

tcf(c_23335,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_23198,c_17001]) ).

tcf(c_23439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_23297,c_17633]) ).

tcf(c_23440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_23297,c_17001]) ).

tcf(c_23791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_23303,c_17633]) ).

tcf(c_23792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_23303,c_17001]) ).

tcf(c_23828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4)),
    inference(superposition,[status(thm)],[c_22943,c_840]) ).

tcf(c_23948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),
    inference(superposition,[status(thm)],[c_23828,c_841]) ).

tcf(c_23955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_23948,c_768]) ).

tcf(c_24112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_21886,c_840]) ).

tcf(c_24305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_21910,c_840]) ).

tcf(c_24867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_23306,c_841]) ).

tcf(c_24873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_23307,c_841]) ).

tcf(c_24879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_23334,c_841]) ).

tcf(c_24894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_23335,c_841]) ).

tcf(c_24901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_23439,c_841]) ).

tcf(c_24969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_23440,c_841]) ).

tcf(c_24975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_23791,c_841]) ).

tcf(c_24981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_23792,c_841]) ).

tcf(c_24989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_24112,c_841]) ).

tcf(c_24996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_24305,c_841]) ).

tcf(c_31240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_20895,c_768]) ).

tcf(c_31365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_31240,c_840]) ).

tcf(c_31541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_31365,c_841]) ).

tcf(c_31649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_20900,c_768]) ).

tcf(c_31778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_31649,c_840]) ).

tcf(c_31853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_31778,c_841]) ).

tcf(c_32282,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_16768,c_770]) ).

tcf(c_55126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X0,X1),c_Pair(X2,X3,X4,X5)),X4,X5),X2)),
    inference(superposition,[status(thm)],[c_21873,c_840]) ).

tcf(c_55454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X0)),
    inference(superposition,[status(thm)],[c_21877,c_840]) ).

tcf(c_55687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X0)),
    inference(superposition,[status(thm)],[c_21889,c_840]) ).

tcf(c_55899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_23955,c_840]) ).

tcf(c_80416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24867,c_633]) ).

tcf(c_80417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24873,c_633]) ).

tcf(c_80418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24879,c_633]) ).

tcf(c_80419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24894,c_633]) ).

tcf(c_80420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24901,c_633]) ).

tcf(c_80422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24969,c_633]) ).

tcf(c_80423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24975,c_633]) ).

tcf(c_80424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24981,c_633]) ).

tcf(c_80426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24989,c_633]) ).

tcf(c_80427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_24996,c_633]) ).

tcf(c_80435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_31541,c_633]) ).

tcf(c_80436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_31853,c_633]) ).

tcf(c_80500,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80436,c_31853]) ).

tcf(c_80501,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80435,c_31541]) ).

tcf(c_80502,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80427,c_24996]) ).

tcf(c_80503,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80426,c_24989]) ).

tcf(c_80504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80424,c_24981]) ).

tcf(c_80505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80423,c_24975]) ).

tcf(c_80506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80422,c_24969]) ).

tcf(c_80507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80420,c_24901]) ).

tcf(c_80508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80419,c_24894]) ).

tcf(c_80509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80418,c_24879]) ).

tcf(c_80510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80417,c_24873]) ).

tcf(c_80511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_80416,c_24867]) ).

tcf(c_97184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X4,X5),X6),
    inference(superposition,[status(thm)],[c_55126,c_841]) ).

tcf(c_97186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),
    inference(superposition,[status(thm)],[c_55454,c_841]) ).

tcf(c_97187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),
    inference(superposition,[status(thm)],[c_55687,c_841]) ).

tcf(c_97192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_55899,c_841]) ).

tcf(c_125311,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2),
    inference(demodulation,[status(thm)],[c_32282,c_596]) ).

tcf(c_125312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),
    inference(superposition,[status(thm)],[c_7267,c_97184]) ).

tcf(c_125313,plain,
    ! [X0: $i] : hBOOL(hAPP(hAPP(iPr_def_14,X0),X0)),
    inference(superposition,[status(thm)],[c_7267,c_857]) ).

tcf(c_125314,plain,
    ! [X0: $i] : c_List_Olist__all2(iPr_def_14,X0,X0,tc_Type_Oty,tc_Type_Oty),
    inference(superposition,[status(thm)],[c_7267,c_862]) ).

tcf(c_125319,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_125311,c_840]) ).

tcf(c_125320,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80500,c_840]) ).

tcf(c_125321,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X0,X1),c_Pair(X2,X3,X4,X5)),X4,X5),X2)),
    inference(superposition,[status(thm)],[c_97184,c_840]) ).

tcf(c_125322,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X0)),
    inference(superposition,[status(thm)],[c_97186,c_840]) ).

tcf(c_125323,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X0)),
    inference(superposition,[status(thm)],[c_97187,c_840]) ).

tcf(c_125330,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),
    inference(superposition,[status(thm)],[c_857,c_841]) ).

tcf(c_125331,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,hAPP(c_fequal(X1),X0),X2),
    inference(superposition,[status(thm)],[c_866,c_841]) ).

tcf(c_125332,plain,
    ! [X0: $i,X1: $i] : c_in(X0,hAPP(iPr_def_14,X0),X1),
    inference(superposition,[status(thm)],[c_125313,c_841]) ).

tcf(c_125333,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_97192,c_840]) ).

tcf(c_125334,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80501,c_840]) ).

tcf(c_125336,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80502,c_840]) ).

tcf(c_125338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80503,c_840]) ).

tcf(c_125349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_626,c_80502]) ).

tcf(c_125352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80504,c_840]) ).

tcf(c_125354,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_670,c_125311]) ).

tcf(c_125356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80503]) ).

tcf(c_125360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80505]) ).

tcf(c_125362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80505,c_840]) ).

tcf(c_125365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80506]) ).

tcf(c_125367,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80506,c_840]) ).

tcf(c_125370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80507]) ).

tcf(c_125371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80507]) ).

tcf(c_125373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80507,c_840]) ).

tcf(c_125378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80508,c_840]) ).

tcf(c_125381,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_125354,c_840]) ).

tcf(c_125383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_125381,c_841]) ).

tcf(c_125410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80509]) ).

tcf(c_125414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80509,c_840]) ).

tcf(c_125420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80510,c_840]) ).

tcf(c_125422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_698,c_80511]) ).

tcf(c_125426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80511,c_840]) ).

tcf(c_125440,plain,
    c_TypeSafe__Mirabelle_Osconf(v_P,v_E,v_s),
    inference(superposition,[status(thm)],[c_7269,c_854]) ).

tcf(c_125454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X2,X2),X3),
    inference(superposition,[status(thm)],[c_743,c_97186]) ).

tcf(c_125466,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(X2,X2,X1,X1))),
    inference(superposition,[status(thm)],[c_846,c_840]) ).

tcf(c_125474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),X3),
    inference(superposition,[status(thm)],[c_125466,c_841]) ).

tcf(c_125492,plain,
    ! [X0: $i,X1: $i] : c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1) = c_Transitive__Closure_Ortrancl(X0,X1),
    inference(superposition,[status(thm)],[c_596,c_670]) ).

tcf(c_125493,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_732]) ).

tcf(c_125494,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_731]) ).

tcf(c_125502,plain,
    ! [X0: $i,X1: $i] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1) = c_Transitive__Closure_Otrancl(X0,X1),
    inference(superposition,[status(thm)],[c_687,c_670]) ).

tcf(c_125503,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_732]) ).

tcf(c_125504,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_731]) ).

tcf(c_125514,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_125493]) ).

tcf(c_125517,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_125493]) ).

tcf(c_125526,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_125494]) ).

tcf(c_125529,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_125494]) ).

tcf(c_125564,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_840]) ).

tcf(c_125571,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_125564]) ).

tcf(c_125572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X2)),
    inference(superposition,[status(thm)],[c_125330,c_125564]) ).

tcf(c_125573,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X1)),
    inference(superposition,[status(thm)],[c_125331,c_125564]) ).

tcf(c_125574,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X0)),
    inference(superposition,[status(thm)],[c_125332,c_125564]) ).

tcf(c_125575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),c_Pair(X3,X3,X1,X1))),
    inference(superposition,[status(thm)],[c_125474,c_125564]) ).

tcf(c_125576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_125383,c_125564]) ).

tcf(c_125577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X0)),
    inference(superposition,[status(thm)],[c_125312,c_125564]) ).

tcf(c_125578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80500,c_125564]) ).

tcf(c_125579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80501,c_125564]) ).

tcf(c_125580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80502,c_125564]) ).

tcf(c_125581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80503,c_125564]) ).

tcf(c_125582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80504,c_125564]) ).

tcf(c_125583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80505,c_125564]) ).

tcf(c_125584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80506,c_125564]) ).

tcf(c_125585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80507,c_125564]) ).

tcf(c_125586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80508,c_125564]) ).

tcf(c_125587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80509,c_125564]) ).

tcf(c_125588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80510,c_125564]) ).

tcf(c_125589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X4),c_Pair(X5,X6,X4,X4))),
    inference(superposition,[status(thm)],[c_80511,c_125564]) ).

tcf(c_125590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X0,X1),c_Pair(X2,X3,X4,X5)),X4,X5),X6),X2)),
    inference(superposition,[status(thm)],[c_97184,c_125564]) ).

tcf(c_125591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X0)),
    inference(superposition,[status(thm)],[c_97186,c_125564]) ).

tcf(c_125592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X0)),
    inference(superposition,[status(thm)],[c_97187,c_125564]) ).

tcf(c_125593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_97192,c_125564]) ).

tcf(c_125608,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),
    inference(superposition,[status(thm)],[c_125574,c_841]) ).

tcf(c_125639,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_125503]) ).

tcf(c_125642,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_125503]) ).

tcf(c_125651,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_125504]) ).

tcf(c_125654,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_125504]) ).

tcf(c_125672,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X0)),
    inference(superposition,[status(thm)],[c_125608,c_125564]) ).

tcf(c_125674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),
    inference(superposition,[status(thm)],[c_125573,c_841]) ).

tcf(c_125675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X1)),
    inference(superposition,[status(thm)],[c_125674,c_125564]) ).

tcf(c_125678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),
    inference(superposition,[status(thm)],[c_125572,c_841]) ).

tcf(c_125679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),
    inference(superposition,[status(thm)],[c_125672,c_841]) ).

tcf(c_125681,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X2)),
    inference(superposition,[status(thm)],[c_125678,c_125564]) ).

tcf(c_125683,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_125679,c_125564]) ).

tcf(c_125687,plain,
    ! [X0: $i] : hBOOL(hAPP(hAPP(iPr_def_14,X0),X0)),
    inference(superposition,[status(thm)],[c_7267,c_857]) ).

tcf(c_125697,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),
    inference(superposition,[status(thm)],[c_857,c_841]) ).

tcf(c_125698,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,hAPP(c_fequal(X1),X0),X2),
    inference(superposition,[status(thm)],[c_866,c_841]) ).

tcf(c_125699,plain,
    ! [X0: $i,X1: $i] : c_in(X0,hAPP(iPr_def_14,X0),X1),
    inference(superposition,[status(thm)],[c_125687,c_841]) ).

tcf(c_125700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_125319,c_841]) ).

tcf(c_125701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X7),
    inference(superposition,[status(thm)],[c_125320,c_841]) ).

tcf(c_125709,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_670,c_125319]) ).

tcf(c_125711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_125709,c_841]) ).

tcf(c_125715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_698,c_125320]) ).

tcf(c_125717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X0)),
    inference(superposition,[status(thm)],[c_7267,c_125321]) ).

tcf(c_125724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_853,c_125320]) ).

tcf(c_125746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_125576,c_841]) ).

tcf(c_125747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),
    inference(superposition,[status(thm)],[c_125675,c_841]) ).

tcf(c_125769,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X2,X2),X0)),
    inference(superposition,[status(thm)],[c_743,c_125322]) ).

tcf(c_125778,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(X2,X2,X1,X1))),
    inference(superposition,[status(thm)],[c_846,c_840]) ).

tcf(c_125781,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),X3),
    inference(superposition,[status(thm)],[c_125778,c_841]) ).

tcf(c_125790,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2),
    inference(demodulation,[status(thm)],[c_32282,c_596]) ).

tcf(c_125794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),
    inference(superposition,[status(thm)],[c_125575,c_841]) ).

tcf(c_125795,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X0)),
    inference(superposition,[status(thm)],[c_7267,c_125681]) ).

tcf(c_125796,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),
    inference(superposition,[status(thm)],[c_125681,c_841]) ).

tcf(c_125797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),
    inference(superposition,[status(thm)],[c_125795,c_841]) ).

tcf(c_125799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_125683,c_841]) ).

tcf(c_125804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X7),
    inference(superposition,[status(thm)],[c_125334,c_841]) ).

tcf(c_125827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X7),
    inference(superposition,[status(thm)],[c_125336,c_841]) ).

tcf(c_125830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),
    inference(superposition,[status(thm)],[c_125717,c_841]) ).

tcf(c_125832,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),
    inference(superposition,[status(thm)],[c_626,c_596]) ).

tcf(c_125833,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),
    inference(superposition,[status(thm)],[c_853,c_596]) ).

tcf(c_125835,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_732]) ).

tcf(c_125836,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_731]) ).

tcf(c_125841,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1) = c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),
    inference(light_normalisation,[status(thm)],[c_125833,c_596]) ).

tcf(c_125842,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1) = c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),
    inference(light_normalisation,[status(thm)],[c_125832,c_596,c_687]) ).

tcf(c_125847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X7),
    inference(superposition,[status(thm)],[c_125338,c_841]) ).

tcf(c_125849,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),
    inference(superposition,[status(thm)],[c_698,c_687]) ).

tcf(c_125851,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_732]) ).

tcf(c_125852,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_731]) ).

tcf(c_125857,plain,
    ! [X0: $i,X1: $i] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1) = c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),
    inference(light_normalisation,[status(thm)],[c_125849,c_596]) ).

tcf(c_125887,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_840]) ).

tcf(c_125890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_853,c_125352]) ).

tcf(c_125893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125352,c_841]) ).

tcf(c_125916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X2)),
    inference(superposition,[status(thm)],[c_125697,c_125887]) ).

tcf(c_125917,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X1)),
    inference(superposition,[status(thm)],[c_125698,c_125887]) ).

tcf(c_125918,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X0)),
    inference(superposition,[status(thm)],[c_125699,c_125887]) ).

tcf(c_125921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_125747,c_125887]) ).

tcf(c_125922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_125794,c_125887]) ).

tcf(c_125923,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_125796,c_125887]) ).

tcf(c_125924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_125799,c_125887]) ).

tcf(c_125926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_125746,c_125887]) ).

tcf(c_125928,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),
    inference(superposition,[status(thm)],[c_125918,c_841]) ).

tcf(c_125931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),
    inference(superposition,[status(thm)],[c_125917,c_841]) ).

tcf(c_125935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),
    inference(superposition,[status(thm)],[c_125916,c_841]) ).

tcf(c_125939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_125921,c_841]) ).

tcf(c_125942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_125926,c_841]) ).

tcf(c_125943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_125939,c_125887]) ).

tcf(c_125947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_125942,c_125887]) ).

tcf(c_125952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_125922,c_841]) ).

tcf(c_125953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_698,c_125362]) ).

tcf(c_125954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_853,c_125362]) ).

tcf(c_125957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125362,c_841]) ).

tcf(c_125970,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_844]) ).

tcf(c_125972,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_125887]) ).

tcf(c_125973,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_840]) ).

tcf(c_125992,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_125973]) ).

tcf(c_125993,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_125973]) ).

tcf(c_125994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X2)),
    inference(superposition,[status(thm)],[c_125697,c_125973]) ).

tcf(c_125995,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X1)),
    inference(superposition,[status(thm)],[c_125698,c_125973]) ).

tcf(c_125996,plain,
    ! [X0: $i,X1: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X0)),
    inference(superposition,[status(thm)],[c_125699,c_125973]) ).

tcf(c_125997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),c_Pair(X3,X3,X1,X1))),
    inference(superposition,[status(thm)],[c_125781,c_125973]) ).

tcf(c_125998,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X0)),
    inference(superposition,[status(thm)],[c_125928,c_125973]) ).

tcf(c_125999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X1)),
    inference(superposition,[status(thm)],[c_125931,c_125973]) ).

tcf(c_126000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X2)),
    inference(superposition,[status(thm)],[c_125935,c_125973]) ).

tcf(c_126001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_125797,c_125973]) ).

tcf(c_126002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_125747,c_125973]) ).

tcf(c_126003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_125794,c_125973]) ).

tcf(c_126004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_125796,c_125973]) ).

tcf(c_126005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_125799,c_125973]) ).

tcf(c_126006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_125939,c_125973]) ).

tcf(c_126007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_125711,c_125973]) ).

tcf(c_126008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_125746,c_125973]) ).

tcf(c_126009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_125942,c_125973]) ).

tcf(c_126010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X0)),
    inference(superposition,[status(thm)],[c_125830,c_125973]) ).

tcf(c_126015,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),
    inference(superposition,[status(thm)],[c_125996,c_841]) ).

tcf(c_126016,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X0)),
    inference(superposition,[status(thm)],[c_126015,c_125973]) ).

tcf(c_126017,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X0)),
    inference(superposition,[status(thm)],[c_126015,c_125887]) ).

tcf(c_126019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),
    inference(superposition,[status(thm)],[c_125995,c_841]) ).

tcf(c_126020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X1)),
    inference(superposition,[status(thm)],[c_126019,c_125973]) ).

tcf(c_126021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X1)),
    inference(superposition,[status(thm)],[c_126019,c_125887]) ).

tcf(c_126024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),
    inference(superposition,[status(thm)],[c_125994,c_841]) ).

tcf(c_126026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),
    inference(superposition,[status(thm)],[c_125998,c_841]) ).

tcf(c_126028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),
    inference(superposition,[status(thm)],[c_126016,c_841]) ).

tcf(c_126030,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),
    inference(superposition,[status(thm)],[c_126017,c_841]) ).

tcf(c_126032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X2)),
    inference(superposition,[status(thm)],[c_126024,c_125973]) ).

tcf(c_126033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X2)),
    inference(superposition,[status(thm)],[c_126024,c_125887]) ).

tcf(c_126036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_126026,c_125973]) ).

tcf(c_126037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_126026,c_125887]) ).

tcf(c_126040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_126028,c_125973]) ).

tcf(c_126041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_126028,c_125887]) ).

tcf(c_126047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125367,c_841]) ).

tcf(c_126070,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_WellTypeRT_OWTrt(X0,X5,X1,X3,X4)
      | ~ c_Objects_Ohext(c_State_Ohp(X2),X5)
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X1,X2,X3,X4) ),
    inference(superposition,[status(thm)],[c_856,c_538]) ).

tcf(c_126075,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_126030,c_125973]) ).

tcf(c_126076,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X0)),
    inference(superposition,[status(thm)],[c_126030,c_125887]) ).

tcf(c_126079,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),
    inference(superposition,[status(thm)],[c_125999,c_841]) ).

tcf(c_126082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_126007,c_841]) ).

tcf(c_126084,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126020,c_841]) ).

tcf(c_126086,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126021,c_841]) ).

tcf(c_126088,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_126079,c_125973]) ).

tcf(c_126089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_126079,c_125887]) ).

tcf(c_126093,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_126082,c_125973]) ).

tcf(c_126094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_126082,c_125887]) ).

tcf(c_126097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_126084,c_125973]) ).

tcf(c_126098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_126084,c_125887]) ).

tcf(c_126101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_126086,c_125973]) ).

tcf(c_126102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X1)),
    inference(superposition,[status(thm)],[c_126086,c_125887]) ).

tcf(c_126107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),
    inference(superposition,[status(thm)],[c_125997,c_841]) ).

tcf(c_126110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126000,c_841]) ).

tcf(c_126112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126001,c_841]) ).

tcf(c_126113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_698,c_125373]) ).

tcf(c_126118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125373,c_841]) ).

tcf(c_126143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126032,c_841]) ).

tcf(c_126146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126033,c_841]) ).

tcf(c_126149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126036,c_841]) ).

tcf(c_126152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126037,c_841]) ).

tcf(c_126155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126040,c_841]) ).

tcf(c_126158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126041,c_841]) ).

tcf(c_126161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126075,c_841]) ).

tcf(c_126163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),
    inference(superposition,[status(thm)],[c_126076,c_841]) ).

tcf(c_126167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_126107,c_125973]) ).

tcf(c_126168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),c_Pair(X4,X4,X1,X1))),
    inference(superposition,[status(thm)],[c_126107,c_125887]) ).

tcf(c_126172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_126110,c_125973]) ).

tcf(c_126173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_126110,c_125887]) ).

tcf(c_126176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126112,c_125973]) ).

tcf(c_126177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126112,c_125887]) ).

tcf(c_126181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_126143,c_125973]) ).

tcf(c_126182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_126143,c_125887]) ).

tcf(c_126186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125378,c_841]) ).

tcf(c_126209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_126146,c_125973]) ).

tcf(c_126210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X2)),
    inference(superposition,[status(thm)],[c_126146,c_125887]) ).

tcf(c_126214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126149,c_125973]) ).

tcf(c_126215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126149,c_125887]) ).

tcf(c_126219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126152,c_125973]) ).

tcf(c_126220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126152,c_125887]) ).

tcf(c_126224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126155,c_125973]) ).

tcf(c_126225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126155,c_125887]) ).

tcf(c_126229,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126158,c_125973]) ).

tcf(c_126230,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126158,c_125887]) ).

tcf(c_126234,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126161,c_125973]) ).

tcf(c_126235,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126161,c_125887]) ).

tcf(c_126238,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126163,c_125973]) ).

tcf(c_126239,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X0)),
    inference(superposition,[status(thm)],[c_126163,c_125887]) ).

tcf(c_126242,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126002,c_841]) ).

tcf(c_126246,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126008,c_841]) ).

tcf(c_126249,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126088,c_841]) ).

tcf(c_126252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126089,c_841]) ).

tcf(c_126256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126093,c_841]) ).

tcf(c_126257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_698,c_125414]) ).

tcf(c_126261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125414,c_841]) ).

tcf(c_126286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126094,c_841]) ).

tcf(c_126289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126097,c_841]) ).

tcf(c_126292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126098,c_841]) ).

tcf(c_126295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126101,c_841]) ).

tcf(c_126297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126102,c_841]) ).

tcf(c_126299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126242,c_125973]) ).

tcf(c_126300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126242,c_125887]) ).

tcf(c_126305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126246,c_125973]) ).

tcf(c_126306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126246,c_125887]) ).

tcf(c_126310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126249,c_125973]) ).

tcf(c_126311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126249,c_125887]) ).

tcf(c_126315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126252,c_125973]) ).

tcf(c_126316,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126252,c_125887]) ).

tcf(c_126321,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126256,c_125973]) ).

tcf(c_126322,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126256,c_125887]) ).

tcf(c_126327,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126286,c_125973]) ).

tcf(c_126328,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126286,c_125887]) ).

tcf(c_126332,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126289,c_125973]) ).

tcf(c_126333,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126289,c_125887]) ).

tcf(c_126338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125420,c_841]) ).

tcf(c_126349,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X1,X2),X2),c_Pair(X0,X0,X2,X2)))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_125973]) ).

tcf(c_126350,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_OId__on(X1,X2),X2),c_Pair(X0,X0,X2,X2)))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_125887]) ).

tcf(c_126352,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_OId__on(X1,X2),c_Pair(X0,X0,X2,X2)))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_840]) ).

tcf(c_126369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126292,c_125973]) ).

tcf(c_126370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126292,c_125887]) ).

tcf(c_126374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126295,c_125973]) ).

tcf(c_126375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126295,c_125887]) ).

tcf(c_126378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126297,c_125973]) ).

tcf(c_126379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X1)),
    inference(superposition,[status(thm)],[c_126297,c_125887]) ).

tcf(c_126382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_125923,c_841]) ).

tcf(c_126383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_125924,c_841]) ).

tcf(c_126387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_125952,c_125973]) ).

tcf(c_126388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_125952,c_125887]) ).

tcf(c_126394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126003,c_841]) ).

tcf(c_126397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126004,c_841]) ).

tcf(c_126399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126005,c_841]) ).

tcf(c_126404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126167,c_841]) ).

tcf(c_126409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126168,c_841]) ).

tcf(c_126413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126172,c_841]) ).

tcf(c_126414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_698,c_125426]) ).

tcf(c_126418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X7),
    inference(superposition,[status(thm)],[c_125426,c_841]) ).

tcf(c_126431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125709,c_517]) ).

tcf(c_126432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126007,c_517]) ).

tcf(c_126433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125576,c_517]) ).

tcf(c_126434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126093,c_517]) ).

tcf(c_126435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126094,c_517]) ).

tcf(c_126436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126008,c_517]) ).

tcf(c_126437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125926,c_517]) ).

tcf(c_126438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6,X7),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125333,c_517]) ).

tcf(c_126449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_768]) ).

tcf(c_126450,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_768]) ).

tcf(c_126451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_768]) ).

tcf(c_126452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X4,X5),X4),
    inference(superposition,[status(thm)],[c_125697,c_768]) ).

tcf(c_126453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X3,X4),X3),
    inference(superposition,[status(thm)],[c_125698,c_768]) ).

tcf(c_126454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_125699,c_768]) ).

tcf(c_126455,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_125781,c_768]) ).

tcf(c_126456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X2),
    inference(superposition,[status(thm)],[c_125928,c_768]) ).

tcf(c_126457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X3,X4),X3),
    inference(superposition,[status(thm)],[c_125931,c_768]) ).

tcf(c_126458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X4,X5),X4),
    inference(superposition,[status(thm)],[c_125935,c_768]) ).

tcf(c_126459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X2,X3),X2),
    inference(superposition,[status(thm)],[c_125797,c_768]) ).

tcf(c_126460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_125747,c_768]) ).

tcf(c_126461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),
    inference(superposition,[status(thm)],[c_125794,c_768]) ).

tcf(c_126462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X4,X5),X4),
    inference(superposition,[status(thm)],[c_125796,c_768]) ).

tcf(c_126463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_125799,c_768]) ).

tcf(c_126464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_125939,c_768]) ).

tcf(c_126465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_125952,c_768]) ).

tcf(c_126466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126015,c_768]) ).

tcf(c_126467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126019,c_768]) ).

tcf(c_126468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126024,c_768]) ).

tcf(c_126469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126026,c_768]) ).

tcf(c_126470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126028,c_768]) ).

tcf(c_126471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126030,c_768]) ).

tcf(c_126472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126079,c_768]) ).

tcf(c_126473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126084,c_768]) ).

tcf(c_126474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126086,c_768]) ).

tcf(c_126475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126107,c_768]) ).

tcf(c_126476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126110,c_768]) ).

tcf(c_126477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126112,c_768]) ).

tcf(c_126478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126143,c_768]) ).

tcf(c_126479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126146,c_768]) ).

tcf(c_126480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126242,c_768]) ).

tcf(c_126481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126149,c_768]) ).

tcf(c_126482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126152,c_768]) ).

tcf(c_126483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126155,c_768]) ).

tcf(c_126484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126158,c_768]) ).

tcf(c_126485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126161,c_768]) ).

tcf(c_126486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126163,c_768]) ).

tcf(c_126487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126249,c_768]) ).

tcf(c_126488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126252,c_768]) ).

tcf(c_126489,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126289,c_768]) ).

tcf(c_126490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126292,c_768]) ).

tcf(c_126491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126295,c_768]) ).

tcf(c_126492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126297,c_768]) ).

tcf(c_126493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X3),
    inference(superposition,[status(thm)],[c_125711,c_768]) ).

tcf(c_126494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126082,c_768]) ).

tcf(c_126495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X4),
    inference(superposition,[status(thm)],[c_125746,c_768]) ).

tcf(c_126496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126256,c_768]) ).

tcf(c_126497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126286,c_768]) ).

tcf(c_126498,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126246,c_768]) ).

tcf(c_126499,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_125942,c_768]) ).

tcf(c_126500,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X3),X4,X5,X6)),X5,X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_125830,c_768]) ).

tcf(c_126501,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(X2,iPr_def_11,iPr_def_12),iPr_def_11)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,iPr_def_13) ),
    inference(superposition,[status(thm)],[c_7266,c_768]) ).

tcf(c_126512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_126461,c_125973]) ).

tcf(c_126513,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_126461,c_125887]) ).

tcf(c_126514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126461,c_768]) ).

tcf(c_126515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_126461,c_840]) ).

tcf(c_126519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_126475,c_125973]) ).

tcf(c_126520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_126475,c_125887]) ).

tcf(c_126521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126475,c_768]) ).

tcf(c_126522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_126475,c_840]) ).

tcf(c_126528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),
    inference(superposition,[status(thm)],[c_126515,c_841]) ).

tcf(c_126533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),
    inference(superposition,[status(thm)],[c_126522,c_841]) ).

tcf(c_126538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_126528,c_125973]) ).

tcf(c_126539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_126528,c_125887]) ).

tcf(c_126540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126528,c_768]) ).

tcf(c_126545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_126533,c_125973]) ).

tcf(c_126546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_126533,c_125887]) ).

tcf(c_126547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126533,c_768]) ).

tcf(c_126551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),tc_prod(X2,X2),X3),X2),X4)),
    inference(superposition,[status(thm)],[c_126493,c_125973]) ).

tcf(c_126552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),tc_prod(X2,X2),X3),X2),X4)),
    inference(superposition,[status(thm)],[c_126493,c_125887]) ).

tcf(c_126553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),tc_prod(X3,X4),X5),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126493,c_768]) ).

tcf(c_126554,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4)),
    inference(superposition,[status(thm)],[c_126493,c_840]) ).

tcf(c_126558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),
    inference(superposition,[status(thm)],[c_126554,c_841]) ).

tcf(c_126561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126558,c_125973]) ).

tcf(c_126562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126558,c_125887]) ).

tcf(c_126563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126558,c_768]) ).

tcf(c_126569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_126465,c_125973]) ).

tcf(c_126570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_126465,c_125887]) ).

tcf(c_126571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126465,c_768]) ).

tcf(c_126572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_126465,c_840]) ).

tcf(c_126578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_126538,c_841]) ).

tcf(c_126584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_126539,c_841]) ).

tcf(c_126585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),
    inference(superposition,[status(thm)],[c_125577,c_841]) ).

tcf(c_126592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125709,c_537]) ).

tcf(c_126593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126007,c_537]) ).

tcf(c_126594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125576,c_537]) ).

tcf(c_126595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126515,c_537]) ).

tcf(c_126596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126522,c_537]) ).

tcf(c_126597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126093,c_537]) ).

tcf(c_126598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126094,c_537]) ).

tcf(c_126599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126008,c_537]) ).

tcf(c_126600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125926,c_537]) ).

tcf(c_126601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126538,c_537]) ).

tcf(c_126602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126539,c_537]) ).

tcf(c_126603,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_126554,c_537]) ).

tcf(c_126604,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7,X8),X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125333,c_537]) ).

tcf(c_126609,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,X1),X2,X1,X1))) ),
    inference(superposition,[status(thm)],[c_563,c_125973]) ).

tcf(c_126610,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X1),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,X1),X2,X1,X1))) ),
    inference(superposition,[status(thm)],[c_563,c_125887]) ).

tcf(c_126611,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X0,X1),X2,X1),X0,X1) ),
    inference(superposition,[status(thm)],[c_563,c_772]) ).

tcf(c_126612,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X0,X1),X2,X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_563,c_635]) ).

tcf(c_126613,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),c_Relation_ODomain(X0,X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_563,c_768]) ).

tcf(c_126614,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | hBOOL(hAPP(X0,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),X1,X2,X2))) ),
    inference(superposition,[status(thm)],[c_563,c_840]) ).

tcf(c_126631,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X1),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,X1),X2,X1,X1))) ),
    inference(superposition,[status(thm)],[c_566,c_125973]) ).

tcf(c_126632,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X1),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,X1),X2,X1,X1))) ),
    inference(superposition,[status(thm)],[c_566,c_125887]) ).

tcf(c_126633,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X0,X1),X2,X1),X0,X1) ),
    inference(superposition,[status(thm)],[c_566,c_772]) ).

tcf(c_126634,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X0,X1),X2,X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_566,c_635]) ).

tcf(c_126635,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Relation_ODomain(X0,X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_566,c_768]) ).

tcf(c_126636,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | hBOOL(hAPP(X0,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2))) ),
    inference(superposition,[status(thm)],[c_566,c_840]) ).

tcf(c_126659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_126545,c_841]) ).

tcf(c_126665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_126546,c_841]) ).

tcf(c_126672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_126572,c_841]) ).

tcf(c_126677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126578,c_125973]) ).

tcf(c_126678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126578,c_125887]) ).

tcf(c_126679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126578,c_768]) ).

tcf(c_126685,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126584,c_125973]) ).

tcf(c_126686,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126584,c_125887]) ).

tcf(c_126687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126584,c_768]) ).

tcf(c_126692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126659,c_125973]) ).

tcf(c_126693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126659,c_125887]) ).

tcf(c_126694,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126659,c_768]) ).

tcf(c_126699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126665,c_125973]) ).

tcf(c_126700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_126665,c_125887]) ).

tcf(c_126701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126665,c_768]) ).

tcf(c_126707,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_126672,c_125973]) ).

tcf(c_126708,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_126672,c_125887]) ).

tcf(c_126709,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126672,c_768]) ).

tcf(c_126714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126173,c_841]) ).

tcf(c_126717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126176,c_841]) ).

tcf(c_126720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126177,c_841]) ).

tcf(c_126724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126181,c_841]) ).

tcf(c_126725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_743,c_125578]) ).

tcf(c_126727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_853,c_125578]) ).

tcf(c_126730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125578,c_841]) ).

tcf(c_126755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126182,c_841]) ).

tcf(c_126759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126209,c_841]) ).

tcf(c_126762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126210,c_841]) ).

tcf(c_126766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126214,c_841]) ).

tcf(c_126770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126215,c_841]) ).

tcf(c_126774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126219,c_841]) ).

tcf(c_126777,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126220,c_841]) ).

tcf(c_126781,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126224,c_841]) ).

tcf(c_126785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126225,c_841]) ).

tcf(c_126789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126229,c_841]) ).

tcf(c_126792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126230,c_841]) ).

tcf(c_126796,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126234,c_841]) ).

tcf(c_126801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125579,c_841]) ).

tcf(c_126822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Product__Type_OSigma(X0,X1,X2,X2),X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Product__Type_OSigma(X0,X1,X2,X2),X3,X2),X0,X2) ),
    inference(superposition,[status(thm)],[c_563,c_765]) ).

tcf(c_126823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Product__Type_OSigma(X0,X1,X2,X2),X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Product__Type_OSigma(X0,X1,X2,X2),X3,X2),X0,X2) ),
    inference(superposition,[status(thm)],[c_566,c_765]) ).

tcf(c_126824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X2,iPr_def_11)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),c_Product__Type_OSigma(X2,X3,iPr_def_11,iPr_def_12),iPr_def_13) ),
    inference(superposition,[status(thm)],[c_7266,c_765]) ).

tcf(c_126834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126235,c_841]) ).

tcf(c_126837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126238,c_841]) ).

tcf(c_126839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),
    inference(superposition,[status(thm)],[c_126239,c_841]) ).

tcf(c_126841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126382,c_125973]) ).

tcf(c_126842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126382,c_125887]) ).

tcf(c_126843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126382,c_768]) ).

tcf(c_126845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126383,c_125973]) ).

tcf(c_126846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126383,c_125887]) ).

tcf(c_126847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126383,c_768]) ).

tcf(c_126853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_126394,c_125973]) ).

tcf(c_126854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_126394,c_125887]) ).

tcf(c_126855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126394,c_768]) ).

tcf(c_126861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_126855,c_125973]) ).

tcf(c_126862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_126855,c_125887]) ).

tcf(c_126863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126855,c_768]) ).

tcf(c_126864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_126855,c_840]) ).

tcf(c_126871,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_126864,c_841]) ).

tcf(c_126876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_126871,c_125973]) ).

tcf(c_126877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_126871,c_125887]) ).

tcf(c_126878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126871,c_768]) ).

tcf(c_126882,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126397,c_125973]) ).

tcf(c_126883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126397,c_125887]) ).

tcf(c_126884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126397,c_768]) ).

tcf(c_126887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126399,c_125973]) ).

tcf(c_126888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126399,c_125887]) ).

tcf(c_126889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126399,c_768]) ).

tcf(c_126895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_126404,c_125973]) ).

tcf(c_126896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_126404,c_125887]) ).

tcf(c_126897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126404,c_768]) ).

tcf(c_126903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125580,c_841]) ).

tcf(c_126918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),X2),X2)
      | hBOOL(hAPP(X0,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),X3,X2),X3,X2,X2)))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,tc_prod(X2,X2)),c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_550]) ).

tcf(c_126919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),X2),X2)
      | hBOOL(hAPP(X0,c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),X3,X2),X3,X2,X2)))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,tc_prod(X2,X2)),c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_550]) ).

tcf(c_126926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_Map_Omap__add(c_Map_Omap__add(X0,c_Map_Omap__add(X1,X2,X3,X4),X3,X4),X5,X3,X4) = c_Map_Omap__add(c_Map_Omap__add(X0,X1,X3,X4),c_Map_Omap__add(X2,X5,X3,X4),X3,X4),
    inference(superposition,[status(thm)],[c_675,c_675]) ).

tcf(c_126934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X3,X2),X0,X2)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_563,c_761]) ).

tcf(c_126935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X3,X2),X0,X2)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_566,c_761]) ).

tcf(c_126936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Otrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_761]) ).

tcf(c_126937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X2)
      | ~ c_in(X3,X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_OId__on(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_771,c_761]) ).

tcf(c_126938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_761]) ).

tcf(c_126939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X5) ),
    inference(superposition,[status(thm)],[c_125697,c_761]) ).

tcf(c_126940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X4) ),
    inference(superposition,[status(thm)],[c_125698,c_761]) ).

tcf(c_126941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3) ),
    inference(superposition,[status(thm)],[c_125699,c_761]) ).

tcf(c_126942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125781,c_761]) ).

tcf(c_126943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3) ),
    inference(superposition,[status(thm)],[c_125928,c_761]) ).

tcf(c_126944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X4) ),
    inference(superposition,[status(thm)],[c_125931,c_761]) ).

tcf(c_126945,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X5) ),
    inference(superposition,[status(thm)],[c_125935,c_761]) ).

tcf(c_126946,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_125797,c_761]) ).

tcf(c_126947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_125747,c_761]) ).

tcf(c_126948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2) ),
    inference(superposition,[status(thm)],[c_125794,c_761]) ).

tcf(c_126949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_125796,c_761]) ).

tcf(c_126950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_125799,c_761]) ).

tcf(c_126951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_125939,c_761]) ).

tcf(c_126952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2) ),
    inference(superposition,[status(thm)],[c_125952,c_761]) ).

tcf(c_126953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126382,c_761]) ).

tcf(c_126954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126383,c_761]) ).

tcf(c_126955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3) ),
    inference(superposition,[status(thm)],[c_126015,c_761]) ).

tcf(c_126956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X4) ),
    inference(superposition,[status(thm)],[c_126019,c_761]) ).

tcf(c_126957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X5) ),
    inference(superposition,[status(thm)],[c_126024,c_761]) ).

tcf(c_126958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_126026,c_761]) ).

tcf(c_126959,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_126028,c_761]) ).

tcf(c_126960,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_126030,c_761]) ).

tcf(c_126961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_126079,c_761]) ).

tcf(c_126962,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_126084,c_761]) ).

tcf(c_126963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_126086,c_761]) ).

tcf(c_126964,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2) ),
    inference(superposition,[status(thm)],[c_126107,c_761]) ).

tcf(c_126965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_126110,c_761]) ).

tcf(c_126966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126112,c_761]) ).

tcf(c_126967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_126143,c_761]) ).

tcf(c_126968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_126146,c_761]) ).

tcf(c_126969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126242,c_761]) ).

tcf(c_126970,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126149,c_761]) ).

tcf(c_126971,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126152,c_761]) ).

tcf(c_126972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126155,c_761]) ).

tcf(c_126973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126158,c_761]) ).

tcf(c_126974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126161,c_761]) ).

tcf(c_126975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126163,c_761]) ).

tcf(c_126976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2) ),
    inference(superposition,[status(thm)],[c_126394,c_761]) ).

tcf(c_126977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126249,c_761]) ).

tcf(c_126978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126252,c_761]) ).

tcf(c_126979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126289,c_761]) ).

tcf(c_126980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126292,c_761]) ).

tcf(c_126981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126295,c_761]) ).

tcf(c_126982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126297,c_761]) ).

tcf(c_126983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126397,c_761]) ).

tcf(c_126984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126399,c_761]) ).

tcf(c_126985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2) ),
    inference(superposition,[status(thm)],[c_126404,c_761]) ).

tcf(c_126986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_125711,c_761]) ).

tcf(c_126987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_126082,c_761]) ).

tcf(c_126988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_125746,c_761]) ).

tcf(c_126989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4) ),
    inference(superposition,[status(thm)],[c_126528,c_761]) ).

tcf(c_126990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4) ),
    inference(superposition,[status(thm)],[c_126533,c_761]) ).

tcf(c_126991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5) ),
    inference(superposition,[status(thm)],[c_126558,c_761]) ).

tcf(c_126992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_126256,c_761]) ).

tcf(c_126993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_126286,c_761]) ).

tcf(c_126994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_126246,c_761]) ).

tcf(c_126995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_125942,c_761]) ).

tcf(c_126996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_126578,c_761]) ).

tcf(c_126997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_126584,c_761]) ).

tcf(c_126998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_126659,c_761]) ).

tcf(c_126999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_126665,c_761]) ).

tcf(c_127000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3) ),
    inference(superposition,[status(thm)],[c_125830,c_761]) ).

tcf(c_127001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_126672,c_761]) ).

tcf(c_127002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_126871,c_761]) ).

tcf(c_127156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_126897,c_125973]) ).

tcf(c_127157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_126897,c_125887]) ).

tcf(c_127158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_126897,c_761]) ).

tcf(c_127159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126897,c_768]) ).

tcf(c_127160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_126897,c_840]) ).

tcf(c_127183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_127160,c_841]) ).

tcf(c_127188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_127183,c_125973]) ).

tcf(c_127189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_127183,c_125887]) ).

tcf(c_127190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_127183,c_761]) ).

tcf(c_127191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_127183,c_768]) ).

tcf(c_127199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_126409,c_125973]) ).

tcf(c_127200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),c_Pair(X5,X5,X1,X1))),
    inference(superposition,[status(thm)],[c_126409,c_125887]) ).

tcf(c_127201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2) ),
    inference(superposition,[status(thm)],[c_126409,c_761]) ).

tcf(c_127202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126409,c_768]) ).

tcf(c_127211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127202,c_125973]) ).

tcf(c_127212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127202,c_125887]) ).

tcf(c_127213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127202,c_761]) ).

tcf(c_127214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127202,c_768]) ).

tcf(c_127215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_127202,c_840]) ).

tcf(c_127225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),
    inference(superposition,[status(thm)],[c_127215,c_841]) ).

tcf(c_127231,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_127225,c_125973]) ).

tcf(c_127232,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_127225,c_125887]) ).

tcf(c_127233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_127225,c_761]) ).

tcf(c_127234,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_127225,c_768]) ).

tcf(c_127241,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126413,c_125973]) ).

tcf(c_127242,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126413,c_125887]) ).

tcf(c_127243,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126413,c_761]) ).

tcf(c_127244,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126413,c_768]) ).

tcf(c_127255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125581,c_841]) ).

tcf(c_127263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X2)
      | c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_563,c_762]) ).

tcf(c_127265,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Otrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_762]) ).

tcf(c_127267,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_762]) ).

tcf(c_127268,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X5) ),
    inference(superposition,[status(thm)],[c_125697,c_762]) ).

tcf(c_127269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X4) ),
    inference(superposition,[status(thm)],[c_125698,c_762]) ).

tcf(c_127270,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3) ),
    inference(superposition,[status(thm)],[c_125699,c_762]) ).

tcf(c_127272,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3) ),
    inference(superposition,[status(thm)],[c_125928,c_762]) ).

tcf(c_127273,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X4) ),
    inference(superposition,[status(thm)],[c_125931,c_762]) ).

tcf(c_127274,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X5) ),
    inference(superposition,[status(thm)],[c_125935,c_762]) ).

tcf(c_127275,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_125797,c_762]) ).

tcf(c_127276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_125747,c_762]) ).

tcf(c_127278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_125796,c_762]) ).

tcf(c_127279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_125799,c_762]) ).

tcf(c_127280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_125939,c_762]) ).

tcf(c_127282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126382,c_762]) ).

tcf(c_127283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126383,c_762]) ).

tcf(c_127284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3) ),
    inference(superposition,[status(thm)],[c_126015,c_762]) ).

tcf(c_127285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X4) ),
    inference(superposition,[status(thm)],[c_126019,c_762]) ).

tcf(c_127286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X5) ),
    inference(superposition,[status(thm)],[c_126024,c_762]) ).

tcf(c_127287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_126026,c_762]) ).

tcf(c_127288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_126028,c_762]) ).

tcf(c_127289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3) ),
    inference(superposition,[status(thm)],[c_126030,c_762]) ).

tcf(c_127290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_126079,c_762]) ).

tcf(c_127291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_126084,c_762]) ).

tcf(c_127292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X4) ),
    inference(superposition,[status(thm)],[c_126086,c_762]) ).

tcf(c_127294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_126110,c_762]) ).

tcf(c_127295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126112,c_762]) ).

tcf(c_127296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_126143,c_762]) ).

tcf(c_127297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X5) ),
    inference(superposition,[status(thm)],[c_126146,c_762]) ).

tcf(c_127298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126242,c_762]) ).

tcf(c_127299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126149,c_762]) ).

tcf(c_127300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126152,c_762]) ).

tcf(c_127301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126155,c_762]) ).

tcf(c_127302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126158,c_762]) ).

tcf(c_127303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126161,c_762]) ).

tcf(c_127304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3) ),
    inference(superposition,[status(thm)],[c_126163,c_762]) ).

tcf(c_127306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126249,c_762]) ).

tcf(c_127307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126252,c_762]) ).

tcf(c_127308,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126289,c_762]) ).

tcf(c_127309,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126292,c_762]) ).

tcf(c_127310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126295,c_762]) ).

tcf(c_127311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X4) ),
    inference(superposition,[status(thm)],[c_126297,c_762]) ).

tcf(c_127312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126397,c_762]) ).

tcf(c_127313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126399,c_762]) ).

tcf(c_127316,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126413,c_762]) ).

tcf(c_127331,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3) ),
    inference(superposition,[status(thm)],[c_125830,c_762]) ).

tcf(c_127474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X2),X3,X2,X2),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X2),X3,X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X1,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ~ c_Relation_Orefl__on(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_763]) ).

tcf(c_127475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X2),X3,X2,X2),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X2),X3,X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X1,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ~ c_Relation_Orefl__on(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_763]) ).

tcf(c_127476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X3,tc_prod(X1,X1),tc_prod(X1,X1)),X2,tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)))
      | ~ c_in(X3,X0,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(X0,X1),X2,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_603,c_763]) ).

tcf(c_127477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(X3,X3,X1,X1),c_Pair(X3,X3,X1,X1),tc_prod(X1,X1),tc_prod(X1,X1)),X2,tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)))
      | ~ c_in(X3,X0,X1)
      | ~ c_Relation_Orefl__on(c_Relation_OId__on(X0,X1),X2,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_771,c_763]) ).

tcf(c_127478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X3,tc_prod(X1,X1),tc_prod(X1,X1)),X2,tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)))
      | ~ c_in(X3,X0,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(X0,X1),X2,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_844,c_763]) ).

tcf(c_127479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X2,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_125697,c_763]) ).

tcf(c_127480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X1,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(hAPP(c_fequal(X0),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_125698,c_763]) ).

tcf(c_127481,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,X0,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(hAPP(iPr_def_14,X0),X1,X2) ),
    inference(superposition,[status(thm)],[c_125699,c_763]) ).

tcf(c_127482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X4,X4,X1,X1),c_Pair(X4,X4,X1,X1),X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_125781,c_763]) ).

tcf(c_127483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X0,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_125928,c_763]) ).

tcf(c_127484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X1,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_125931,c_763]) ).

tcf(c_127485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X2,X2,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_125935,c_763]) ).

tcf(c_127486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X0,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_125797,c_763]) ).

tcf(c_127487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X1,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_125747,c_763]) ).

tcf(c_127488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(X5,X5,X1,X1),c_Pair(X5,X5,X1,X1),X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_125794,c_763]) ).

tcf(c_127489,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X2,X2,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_125796,c_763]) ).

tcf(c_127490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_125799,c_763]) ).

tcf(c_127491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_125939,c_763]) ).

tcf(c_127492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X6,X6,X1,X1),c_Pair(X6,X6,X1,X1),X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_125952,c_763]) ).

tcf(c_127493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126382,c_763]) ).

tcf(c_127494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126383,c_763]) ).

tcf(c_127495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X0,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_126015,c_763]) ).

tcf(c_127496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X1,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_126019,c_763]) ).

tcf(c_127497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X2,X2,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126024,c_763]) ).

tcf(c_127498,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X0,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_126026,c_763]) ).

tcf(c_127499,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X0,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_126028,c_763]) ).

tcf(c_127500,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X0,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_126030,c_763]) ).

tcf(c_127501,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X1,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126079,c_763]) ).

tcf(c_127502,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X1,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126084,c_763]) ).

tcf(c_127503,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X1,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126086,c_763]) ).

tcf(c_127504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(X5,X5,X1,X1),c_Pair(X5,X5,X1,X1),X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_126107,c_763]) ).

tcf(c_127505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X2,X2,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126110,c_763]) ).

tcf(c_127506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126112,c_763]) ).

tcf(c_127507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X2,X2,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126143,c_763]) ).

tcf(c_127508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X2,X2,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126146,c_763]) ).

tcf(c_127509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126242,c_763]) ).

tcf(c_127510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126149,c_763]) ).

tcf(c_127511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126152,c_763]) ).

tcf(c_127512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126155,c_763]) ).

tcf(c_127513,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126158,c_763]) ).

tcf(c_127514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126161,c_763]) ).

tcf(c_127515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126163,c_763]) ).

tcf(c_127516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X6,X6,X1,X1),c_Pair(X6,X6,X1,X1),X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126394,c_763]) ).

tcf(c_127517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126249,c_763]) ).

tcf(c_127518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126252,c_763]) ).

tcf(c_127519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126289,c_763]) ).

tcf(c_127520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126292,c_763]) ).

tcf(c_127521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126295,c_763]) ).

tcf(c_127522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126297,c_763]) ).

tcf(c_127523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126397,c_763]) ).

tcf(c_127524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126399,c_763]) ).

tcf(c_127525,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X6,X6,X1,X1),c_Pair(X6,X6,X1,X1),X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126404,c_763]) ).

tcf(c_127526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X6,X6,X1,X1),c_Pair(X6,X6,X1,X1),X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126409,c_763]) ).

tcf(c_127527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126413,c_763]) ).

tcf(c_127528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_125711,c_763]) ).

tcf(c_127529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_126082,c_763]) ).

tcf(c_127530,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_125746,c_763]) ).

tcf(c_127531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4) ),
    inference(superposition,[status(thm)],[c_126528,c_763]) ).

tcf(c_127532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4) ),
    inference(superposition,[status(thm)],[c_126533,c_763]) ).

tcf(c_127533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126558,c_763]) ).

tcf(c_127534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126256,c_763]) ).

tcf(c_127535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126286,c_763]) ).

tcf(c_127536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126246,c_763]) ).

tcf(c_127537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_125942,c_763]) ).

tcf(c_127538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126578,c_763]) ).

tcf(c_127539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126584,c_763]) ).

tcf(c_127540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126659,c_763]) ).

tcf(c_127541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_126665,c_763]) ).

tcf(c_127542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X0,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_125830,c_763]) ).

tcf(c_127543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_126672,c_763]) ).

tcf(c_127544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_126871,c_763]) ).

tcf(c_127545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_127183,c_763]) ).

tcf(c_127546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_127225,c_763]) ).

tcf(c_127773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Product__Type_OSigma(X2,X1,X3,X3),X3),X3)
      | c_in(X0,hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Product__Type_OSigma(X2,X1,X3,X3),X0,X3)),X3) ),
    inference(superposition,[status(thm)],[c_563,c_766]) ).

tcf(c_127774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Product__Type_OSigma(X2,X1,X3,X3),X3),X3)
      | c_in(X0,hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Product__Type_OSigma(X2,X1,X3,X3),X0,X3)),X3) ),
    inference(superposition,[status(thm)],[c_566,c_766]) ).

tcf(c_127775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,hAPP(X3,X0),iPr_def_12)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),c_Product__Type_OSigma(X2,X3,iPr_def_11,iPr_def_12),iPr_def_13) ),
    inference(superposition,[status(thm)],[c_7266,c_766]) ).

tcf(c_127786,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_563,c_770]) ).

tcf(c_127788,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_770]) ).

tcf(c_127789,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_770]) ).

tcf(c_127790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_770]) ).

tcf(c_127791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_125697,c_770]) ).

tcf(c_127792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_125698,c_770]) ).

tcf(c_127793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_125699,c_770]) ).

tcf(c_127795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_125928,c_770]) ).

tcf(c_127796,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_125931,c_770]) ).

tcf(c_127797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_125935,c_770]) ).

tcf(c_127798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_125797,c_770]) ).

tcf(c_127799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_125747,c_770]) ).

tcf(c_127800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_125794,c_770]) ).

tcf(c_127801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_125796,c_770]) ).

tcf(c_127802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_125799,c_770]) ).

tcf(c_127803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_125939,c_770]) ).

tcf(c_127804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_125952,c_770]) ).

tcf(c_127805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126382,c_770]) ).

tcf(c_127806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126383,c_770]) ).

tcf(c_127807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126015,c_770]) ).

tcf(c_127808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126019,c_770]) ).

tcf(c_127809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126024,c_770]) ).

tcf(c_127810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126026,c_770]) ).

tcf(c_127811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126028,c_770]) ).

tcf(c_127812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126030,c_770]) ).

tcf(c_127813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126079,c_770]) ).

tcf(c_127814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126084,c_770]) ).

tcf(c_127815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126086,c_770]) ).

tcf(c_127816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126107,c_770]) ).

tcf(c_127817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126110,c_770]) ).

tcf(c_127818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126112,c_770]) ).

tcf(c_127819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126143,c_770]) ).

tcf(c_127820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126146,c_770]) ).

tcf(c_127821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126242,c_770]) ).

tcf(c_127822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126149,c_770]) ).

tcf(c_127823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126152,c_770]) ).

tcf(c_127824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126155,c_770]) ).

tcf(c_127825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126158,c_770]) ).

tcf(c_127826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126161,c_770]) ).

tcf(c_127827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126163,c_770]) ).

tcf(c_127828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126394,c_770]) ).

tcf(c_127829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126249,c_770]) ).

tcf(c_127830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126252,c_770]) ).

tcf(c_127831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126289,c_770]) ).

tcf(c_127832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126292,c_770]) ).

tcf(c_127833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126295,c_770]) ).

tcf(c_127834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126297,c_770]) ).

tcf(c_127835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126397,c_770]) ).

tcf(c_127836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126399,c_770]) ).

tcf(c_127837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126404,c_770]) ).

tcf(c_127838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_126409,c_770]) ).

tcf(c_127839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126413,c_770]) ).

tcf(c_127840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_125711,c_770]) ).

tcf(c_127841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126082,c_770]) ).

tcf(c_127842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_125746,c_770]) ).

tcf(c_127843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126528,c_770]) ).

tcf(c_127844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126533,c_770]) ).

tcf(c_127845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126558,c_770]) ).

tcf(c_127846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126256,c_770]) ).

tcf(c_127847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126286,c_770]) ).

tcf(c_127848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126246,c_770]) ).

tcf(c_127849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_125942,c_770]) ).

tcf(c_127850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126578,c_770]) ).

tcf(c_127851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126584,c_770]) ).

tcf(c_127852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126659,c_770]) ).

tcf(c_127853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126665,c_770]) ).

tcf(c_127854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X3),X4,X5,X6)),X5,X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_125830,c_770]) ).

tcf(c_127855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126672,c_770]) ).

tcf(c_127856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126871,c_770]) ).

tcf(c_127857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_127183,c_770]) ).

tcf(c_127858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_127225,c_770]) ).

tcf(c_127859,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X2,iPr_def_11,iPr_def_12),iPr_def_12,iPr_def_11),iPr_def_12)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,iPr_def_13) ),
    inference(superposition,[status(thm)],[c_7266,c_770]) ).

tcf(c_127934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,tc_prod(X3,X3),X4)),tc_prod(X3,X3),X4),X3),X1)),
    inference(superposition,[status(thm)],[c_126453,c_125973]) ).

tcf(c_127935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,tc_prod(X3,X3),X4)),tc_prod(X3,X3),X4),X3),X1)),
    inference(superposition,[status(thm)],[c_126453,c_125887]) ).

tcf(c_127936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4),X6)),tc_prod(X4,X4),X6),X4) ),
    inference(superposition,[status(thm)],[c_126453,c_762]) ).

tcf(c_127937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4),X6)),tc_prod(X4,X4),X6),X4) ),
    inference(superposition,[status(thm)],[c_126453,c_761]) ).

tcf(c_127938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4),X6)),tc_prod(X3,X4),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126453,c_770]) ).

tcf(c_127939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,tc_prod(X3,X4),X6)),tc_prod(X3,X4),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126453,c_768]) ).

tcf(c_127940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X1,X3,X3),X5,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5,X3) ),
    inference(superposition,[status(thm)],[c_126453,c_763]) ).

tcf(c_127941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X1)),
    inference(superposition,[status(thm)],[c_126453,c_840]) ).

tcf(c_127952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126494,c_125973]) ).

tcf(c_127953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126494,c_125887]) ).

tcf(c_127954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X4),X5),X4) ),
    inference(superposition,[status(thm)],[c_126494,c_762]) ).

tcf(c_127956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X5),X6),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126494,c_770]) ).

tcf(c_127957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X5),X6),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126494,c_768]) ).

tcf(c_127958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X3,X3),X5,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5,X3) ),
    inference(superposition,[status(thm)],[c_126494,c_763]) ).

tcf(c_127959,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5)),
    inference(superposition,[status(thm)],[c_126494,c_840]) ).

tcf(c_127969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X3),X3),
    inference(superposition,[status(thm)],[c_743,c_126495]) ).

tcf(c_127972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126495,c_125973]) ).

tcf(c_127973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126495,c_125887]) ).

tcf(c_127974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X4),X5),X4) ),
    inference(superposition,[status(thm)],[c_126495,c_762]) ).

tcf(c_127976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X5),X6),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126495,c_770]) ).

tcf(c_127977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X5),X6),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126495,c_768]) ).

tcf(c_127978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X3,X3),X5,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5,X3) ),
    inference(superposition,[status(thm)],[c_126495,c_763]) ).

tcf(c_127979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5)),
    inference(superposition,[status(thm)],[c_126495,c_840]) ).

tcf(c_127995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126540,c_125973]) ).

tcf(c_127996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126540,c_125887]) ).

tcf(c_127997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X4),X5),X4) ),
    inference(superposition,[status(thm)],[c_126540,c_762]) ).

tcf(c_127999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X5),X6),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126540,c_770]) ).

tcf(c_128000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X5),X6),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126540,c_768]) ).

tcf(c_128001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X3,X3),X5,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5,X3) ),
    inference(superposition,[status(thm)],[c_126540,c_763]) ).

tcf(c_128002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5)),
    inference(superposition,[status(thm)],[c_126540,c_840]) ).

tcf(c_128019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126547,c_125973]) ).

tcf(c_128020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),tc_prod(X3,X3),X4),X3),X5)),
    inference(superposition,[status(thm)],[c_126547,c_125887]) ).

tcf(c_128021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X4),X5),X4) ),
    inference(superposition,[status(thm)],[c_126547,c_762]) ).

tcf(c_128023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X5),X6),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126547,c_770]) ).

tcf(c_128024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X5),X6),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126547,c_768]) ).

tcf(c_128025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X3,X3),X5,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5,X3) ),
    inference(superposition,[status(thm)],[c_126547,c_763]) ).

tcf(c_128026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5)),
    inference(superposition,[status(thm)],[c_126547,c_840]) ).

tcf(c_128047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),
    inference(superposition,[status(thm)],[c_126561,c_841]) ).

tcf(c_128082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),
    inference(superposition,[status(thm)],[c_126562,c_841]) ).

tcf(c_128086,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126714,c_125973]) ).

tcf(c_128087,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126714,c_125887]) ).

tcf(c_128088,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126714,c_762]) ).

tcf(c_128089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126714,c_761]) ).

tcf(c_128090,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126714,c_770]) ).

tcf(c_128091,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126714,c_768]) ).

tcf(c_128092,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126714,c_763]) ).

tcf(c_128102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126717,c_125973]) ).

tcf(c_128103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126717,c_125887]) ).

tcf(c_128104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126717,c_762]) ).

tcf(c_128105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126717,c_761]) ).

tcf(c_128106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126717,c_770]) ).

tcf(c_128107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126717,c_768]) ).

tcf(c_128108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126717,c_763]) ).

tcf(c_128118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126720,c_125973]) ).

tcf(c_128119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126720,c_125887]) ).

tcf(c_128120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126720,c_762]) ).

tcf(c_128121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126720,c_761]) ).

tcf(c_128122,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126720,c_770]) ).

tcf(c_128123,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126720,c_768]) ).

tcf(c_128124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126720,c_763]) ).

tcf(c_128135,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126724,c_125973]) ).

tcf(c_128136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126724,c_125887]) ).

tcf(c_128137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126724,c_762]) ).

tcf(c_128138,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126724,c_761]) ).

tcf(c_128139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126724,c_770]) ).

tcf(c_128140,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126724,c_768]) ).

tcf(c_128141,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126724,c_763]) ).

tcf(c_128152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126755,c_125973]) ).

tcf(c_128153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126755,c_125887]) ).

tcf(c_128154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126755,c_762]) ).

tcf(c_128155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126755,c_761]) ).

tcf(c_128156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126755,c_770]) ).

tcf(c_128157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126755,c_768]) ).

tcf(c_128158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126755,c_763]) ).

tcf(c_128166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_853,c_125582]) ).

tcf(c_128169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125582,c_841]) ).

tcf(c_128190,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_List_Olist__all2(iPr_def_14,c_Conform_Osko__Conform__Xconfs__conv__map__1__1(v_P,X2,X0,X1,iPr_def_13),X2,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_Conform_Oconf(v_P,X0,iPr_def_13),X1,X2,tc_Value_Oval,tc_Type_Oty) ),
    inference(superposition,[status(thm)],[c_7267,c_569]) ).

tcf(c_128193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X0,X1,X2,c_Expr_Oexp_OSeq(X3,X5,iPr_def_10),X6)
      | ~ c_WellTypeRT_OWTrt(X0,X1,X2,X5,X6)
      | ~ c_WellTypeRT_OWTrt(X0,X1,X2,X3,X4) ),
    inference(light_normalisation,[status(thm)],[c_590,c_7263]) ).

tcf(c_128203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,c_Expr_Oexp_OSeq(X5,X3,iPr_def_10),X4)
      | ~ c_TypeSafe__Mirabelle_Owf__config(X0,X2,X1,X5,X6)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,X4) ),
    inference(superposition,[status(thm)],[c_856,c_128193]) ).

tcf(c_128210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126759,c_125973]) ).

tcf(c_128211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126759,c_125887]) ).

tcf(c_128212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126759,c_762]) ).

tcf(c_128213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126759,c_761]) ).

tcf(c_128214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126759,c_770]) ).

tcf(c_128215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126759,c_768]) ).

tcf(c_128216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126759,c_763]) ).

tcf(c_128232,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126762,c_125973]) ).

tcf(c_128233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X2)),
    inference(superposition,[status(thm)],[c_126762,c_125887]) ).

tcf(c_128234,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126762,c_762]) ).

tcf(c_128235,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X5) ),
    inference(superposition,[status(thm)],[c_126762,c_761]) ).

tcf(c_128236,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_126762,c_770]) ).

tcf(c_128237,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_126762,c_768]) ).

tcf(c_128238,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_126762,c_763]) ).

tcf(c_128258,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126766,c_125973]) ).

tcf(c_128259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126766,c_125887]) ).

tcf(c_128260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126766,c_762]) ).

tcf(c_128261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126766,c_761]) ).

tcf(c_128262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126766,c_770]) ).

tcf(c_128263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126766,c_768]) ).

tcf(c_128264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126766,c_763]) ).

tcf(c_128281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126770,c_125973]) ).

tcf(c_128282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126770,c_125887]) ).

tcf(c_128283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126770,c_762]) ).

tcf(c_128284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126770,c_761]) ).

tcf(c_128285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126770,c_770]) ).

tcf(c_128286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126770,c_768]) ).

tcf(c_128287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126770,c_763]) ).

tcf(c_128307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126774,c_125973]) ).

tcf(c_128308,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126774,c_125887]) ).

tcf(c_128309,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126774,c_762]) ).

tcf(c_128310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126774,c_761]) ).

tcf(c_128311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126774,c_770]) ).

tcf(c_128312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126774,c_768]) ).

tcf(c_128313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126774,c_763]) ).

tcf(c_128335,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126777,c_125973]) ).

tcf(c_128336,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126777,c_125887]) ).

tcf(c_128337,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126777,c_762]) ).

tcf(c_128338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126777,c_761]) ).

tcf(c_128339,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126777,c_770]) ).

tcf(c_128340,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126777,c_768]) ).

tcf(c_128341,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126777,c_763]) ).

tcf(c_128352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126781,c_125973]) ).

tcf(c_128353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126781,c_125887]) ).

tcf(c_128354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126781,c_762]) ).

tcf(c_128355,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126781,c_761]) ).

tcf(c_128356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126781,c_770]) ).

tcf(c_128357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126781,c_768]) ).

tcf(c_128358,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126781,c_763]) ).

tcf(c_128378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126785,c_125973]) ).

tcf(c_128379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126785,c_125887]) ).

tcf(c_128380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126785,c_762]) ).

tcf(c_128381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126785,c_761]) ).

tcf(c_128382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126785,c_770]) ).

tcf(c_128383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126785,c_768]) ).

tcf(c_128384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126785,c_763]) ).

tcf(c_128407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126789,c_125973]) ).

tcf(c_128408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126789,c_125887]) ).

tcf(c_128409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126789,c_762]) ).

tcf(c_128410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126789,c_761]) ).

tcf(c_128411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126789,c_770]) ).

tcf(c_128412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126789,c_768]) ).

tcf(c_128413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126789,c_763]) ).

tcf(c_128442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126792,c_125973]) ).

tcf(c_128443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126792,c_125887]) ).

tcf(c_128444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126792,c_762]) ).

tcf(c_128445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126792,c_761]) ).

tcf(c_128446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126792,c_770]) ).

tcf(c_128447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126792,c_768]) ).

tcf(c_128448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126792,c_763]) ).

tcf(c_128459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126796,c_125973]) ).

tcf(c_128460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126796,c_125887]) ).

tcf(c_128461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126796,c_762]) ).

tcf(c_128462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126796,c_761]) ).

tcf(c_128463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126796,c_770]) ).

tcf(c_128464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126796,c_768]) ).

tcf(c_128465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126796,c_763]) ).

tcf(c_128476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126834,c_125973]) ).

tcf(c_128477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126834,c_125887]) ).

tcf(c_128478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126834,c_762]) ).

tcf(c_128479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126834,c_761]) ).

tcf(c_128480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126834,c_770]) ).

tcf(c_128481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126834,c_768]) ).

tcf(c_128482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126834,c_763]) ).

tcf(c_128491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X3),c_Pair(X4,X5,X3,X3))),
    inference(superposition,[status(thm)],[c_853,c_125583]) ).

tcf(c_128494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125583,c_841]) ).

tcf(c_128500,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_Oconverse(X1,X2,X2),X0,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_639]) ).

tcf(c_128501,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_Oconverse(X1,X2,X2),X0,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_639]) ).

tcf(c_128504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_684,c_639]) ).

tcf(c_128505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_687,c_639]) ).

tcf(c_128506,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X1,X0,iPr_def_12,iPr_def_11),X2,tc_prod(iPr_def_12,iPr_def_11))
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),c_Relation_Oconverse(X2,iPr_def_12,iPr_def_11),iPr_def_13) ),
    inference(superposition,[status(thm)],[c_7266,c_639]) ).

tcf(c_128543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_687,c_641]) ).

tcf(c_128544,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X1,X0,iPr_def_11,iPr_def_12),c_Relation_Oconverse(X2,iPr_def_12,iPr_def_11),iPr_def_13)
      | ~ c_in(c_Pair(X0,X1,iPr_def_12,iPr_def_11),X2,tc_prod(iPr_def_12,iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_7266,c_641]) ).

tcf(c_128545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Pair(X1,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_125973]) ).

tcf(c_128546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Pair(X1,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_125887]) ).

tcf(c_128547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Relation_Oconverse(X3,X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_762]) ).

tcf(c_128548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Relation_Oconverse(X3,X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_761]) ).

tcf(c_128550,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Oconverse(X4,X2,X3),X3,X2),X2,X3),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_641,c_770]) ).

tcf(c_128552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(X1,X0,X3,X2),c_Pair(X1,X0,X3,X2),tc_prod(X3,X2),tc_prod(X3,X2)),X5,tc_prod(tc_prod(X3,X2),tc_prod(X3,X2)))
      | ~ c_Relation_Orefl__on(c_Relation_Oconverse(X4,X2,X3),X5,tc_prod(X3,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_641,c_763]) ).

tcf(c_128553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_Oconverse(X4,X2,X3),c_Pair(X1,X0,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_641,c_840]) ).

tcf(c_128581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(X1,c_Relation_OImage(X0,X3,X2,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),X3,X2) ),
    inference(superposition,[status(thm)],[c_563,c_774]) ).

tcf(c_128582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(X1,c_Relation_OImage(X0,X3,X2,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X3,X2) ),
    inference(superposition,[status(thm)],[c_566,c_774]) ).

tcf(c_128583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Relation_OImage(c_Transitive__Closure_Otrancl(X3,X2),X4,X2,X2),X2)
      | ~ c_in(X0,X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_774]) ).

tcf(c_128584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_OImage(c_Relation_Oconverse(X4,X2,X3),X5,X3,X2),X2)
      | ~ c_in(X1,X5,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_641,c_774]) ).

tcf(c_128585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_OImage(c_Relation_OId__on(X1,X2),X3,X2,X2),X2)
      | ~ c_in(X0,X3,X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_774]) ).

tcf(c_128586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X4,X2,X2),X2)
      | ~ c_in(X0,X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_774]) ).

tcf(c_128587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125697,c_774]) ).

tcf(c_128588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,c_Relation_OImage(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125698,c_774]) ).

tcf(c_128589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Relation_OImage(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125699,c_774]) ).

tcf(c_128590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125781,c_774]) ).

tcf(c_128591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125928,c_774]) ).

tcf(c_128592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125931,c_774]) ).

tcf(c_128593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125935,c_774]) ).

tcf(c_128594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125797,c_774]) ).

tcf(c_128595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125747,c_774]) ).

tcf(c_128596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125794,c_774]) ).

tcf(c_128597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125796,c_774]) ).

tcf(c_128598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125799,c_774]) ).

tcf(c_128599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125939,c_774]) ).

tcf(c_128600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125952,c_774]) ).

tcf(c_128601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126382,c_774]) ).

tcf(c_128602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126383,c_774]) ).

tcf(c_128603,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126015,c_774]) ).

tcf(c_128604,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126019,c_774]) ).

tcf(c_128605,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126024,c_774]) ).

tcf(c_128606,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126026,c_774]) ).

tcf(c_128607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126028,c_774]) ).

tcf(c_128608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126030,c_774]) ).

tcf(c_128609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126079,c_774]) ).

tcf(c_128610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126084,c_774]) ).

tcf(c_128611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126086,c_774]) ).

tcf(c_128612,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126107,c_774]) ).

tcf(c_128613,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126110,c_774]) ).

tcf(c_128614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126112,c_774]) ).

tcf(c_128615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126143,c_774]) ).

tcf(c_128616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126146,c_774]) ).

tcf(c_128617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126242,c_774]) ).

tcf(c_128618,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126149,c_774]) ).

tcf(c_128619,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126152,c_774]) ).

tcf(c_128620,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126155,c_774]) ).

tcf(c_128621,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126158,c_774]) ).

tcf(c_128622,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126161,c_774]) ).

tcf(c_128623,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126163,c_774]) ).

tcf(c_128624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126394,c_774]) ).

tcf(c_128625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126249,c_774]) ).

tcf(c_128626,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126252,c_774]) ).

tcf(c_128627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126289,c_774]) ).

tcf(c_128628,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126292,c_774]) ).

tcf(c_128629,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126295,c_774]) ).

tcf(c_128630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126297,c_774]) ).

tcf(c_128631,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126397,c_774]) ).

tcf(c_128632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126399,c_774]) ).

tcf(c_128633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126404,c_774]) ).

tcf(c_128634,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126409,c_774]) ).

tcf(c_128635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126413,c_774]) ).

tcf(c_128636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126714,c_774]) ).

tcf(c_128637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126717,c_774]) ).

tcf(c_128638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126720,c_774]) ).

tcf(c_128639,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126724,c_774]) ).

tcf(c_128640,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126755,c_774]) ).

tcf(c_128641,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126759,c_774]) ).

tcf(c_128642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126762,c_774]) ).

tcf(c_128643,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126766,c_774]) ).

tcf(c_128644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126770,c_774]) ).

tcf(c_128645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126774,c_774]) ).

tcf(c_128646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126777,c_774]) ).

tcf(c_128647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,tc_prod(X2,X5),X7)),tc_prod(X2,X5),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126453,c_774]) ).

tcf(c_128648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125711,c_774]) ).

tcf(c_128649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126082,c_774]) ).

tcf(c_128650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125746,c_774]) ).

tcf(c_128651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126528,c_774]) ).

tcf(c_128652,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126533,c_774]) ).

tcf(c_128653,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),tc_prod(X2,X7),X8),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126494,c_774]) ).

tcf(c_128654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),tc_prod(X2,X7),X8),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126495,c_774]) ).

tcf(c_128655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),tc_prod(X2,X7),X8),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126540,c_774]) ).

tcf(c_128656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126781,c_774]) ).

tcf(c_128657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),tc_prod(X2,X7),X8),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126547,c_774]) ).

tcf(c_128658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126558,c_774]) ).

tcf(c_128659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126256,c_774]) ).

tcf(c_128660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126286,c_774]) ).

tcf(c_128661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126246,c_774]) ).

tcf(c_128662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125942,c_774]) ).

tcf(c_128663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126578,c_774]) ).

tcf(c_128664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126785,c_774]) ).

tcf(c_128665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126584,c_774]) ).

tcf(c_128666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126659,c_774]) ).

tcf(c_128667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126665,c_774]) ).

tcf(c_128668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X4),X5,X6,X7)),X6,X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_125830,c_774]) ).

tcf(c_128669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126672,c_774]) ).

tcf(c_128670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126871,c_774]) ).

tcf(c_128671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126789,c_774]) ).

tcf(c_128672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126792,c_774]) ).

tcf(c_128673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126796,c_774]) ).

tcf(c_128674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126834,c_774]) ).

tcf(c_128675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127183,c_774]) ).

tcf(c_128676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127225,c_774]) ).

tcf(c_128677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_OImage(X2,X3,iPr_def_11,iPr_def_12),iPr_def_12)
      | ~ c_in(X0,X3,iPr_def_11)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,iPr_def_13) ),
    inference(superposition,[status(thm)],[c_7266,c_774]) ).

tcf(c_128958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_776]) ).

tcf(c_128959,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X2,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_776]) ).

tcf(c_128961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_776]) ).

tcf(c_128962,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X4),X4) ),
    inference(superposition,[status(thm)],[c_125697,c_776]) ).

tcf(c_128963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X3),X3) ),
    inference(superposition,[status(thm)],[c_125698,c_776]) ).

tcf(c_128964,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_125699,c_776]) ).

tcf(c_128966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X2),X2) ),
    inference(superposition,[status(thm)],[c_125928,c_776]) ).

tcf(c_128967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X3),X3) ),
    inference(superposition,[status(thm)],[c_125931,c_776]) ).

tcf(c_128968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X4),X4) ),
    inference(superposition,[status(thm)],[c_125935,c_776]) ).

tcf(c_128969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_125797,c_776]) ).

tcf(c_128970,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_125747,c_776]) ).

tcf(c_128972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4) ),
    inference(superposition,[status(thm)],[c_125796,c_776]) ).

tcf(c_128973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_125799,c_776]) ).

tcf(c_128974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_125939,c_776]) ).

tcf(c_128976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126382,c_776]) ).

tcf(c_128977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126383,c_776]) ).

tcf(c_128978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X2),X2) ),
    inference(superposition,[status(thm)],[c_126015,c_776]) ).

tcf(c_128979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X3),X3) ),
    inference(superposition,[status(thm)],[c_126019,c_776]) ).

tcf(c_128980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X4),X4) ),
    inference(superposition,[status(thm)],[c_126024,c_776]) ).

tcf(c_128981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_126026,c_776]) ).

tcf(c_128982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_126028,c_776]) ).

tcf(c_128983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_126030,c_776]) ).

tcf(c_128984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_126079,c_776]) ).

tcf(c_128985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_126084,c_776]) ).

tcf(c_128986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_126086,c_776]) ).

tcf(c_128988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4) ),
    inference(superposition,[status(thm)],[c_126110,c_776]) ).

tcf(c_128989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126112,c_776]) ).

tcf(c_128990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4) ),
    inference(superposition,[status(thm)],[c_126143,c_776]) ).

tcf(c_128991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X4),X4) ),
    inference(superposition,[status(thm)],[c_126146,c_776]) ).

tcf(c_128992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126242,c_776]) ).

tcf(c_128993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126149,c_776]) ).

tcf(c_128994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126152,c_776]) ).

tcf(c_128995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126155,c_776]) ).

tcf(c_128996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126158,c_776]) ).

tcf(c_128997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126161,c_776]) ).

tcf(c_128998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_126163,c_776]) ).

tcf(c_129000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126249,c_776]) ).

tcf(c_129001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126252,c_776]) ).

tcf(c_129002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126289,c_776]) ).

tcf(c_129003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126292,c_776]) ).

tcf(c_129004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126295,c_776]) ).

tcf(c_129005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_126297,c_776]) ).

tcf(c_129006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126397,c_776]) ).

tcf(c_129007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126399,c_776]) ).

tcf(c_129010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126413,c_776]) ).

tcf(c_129011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126714,c_776]) ).

tcf(c_129012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126717,c_776]) ).

tcf(c_129013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126720,c_776]) ).

tcf(c_129014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126724,c_776]) ).

tcf(c_129015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126755,c_776]) ).

tcf(c_129016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126759,c_776]) ).

tcf(c_129017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_126762,c_776]) ).

tcf(c_129018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126766,c_776]) ).

tcf(c_129019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126770,c_776]) ).

tcf(c_129020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126774,c_776]) ).

tcf(c_129021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126777,c_776]) ).

tcf(c_129022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3),X5)),tc_prod(X3,X3),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3),X5)),tc_prod(X3,X3),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_126453,c_776]) ).

tcf(c_129023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_125711,c_776]) ).

tcf(c_129024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_126082,c_776]) ).

tcf(c_129025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_125746,c_776]) ).

tcf(c_129026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_126528,c_776]) ).

tcf(c_129027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_126533,c_776]) ).

tcf(c_129028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X4),X5),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X4),X5),X4),X4) ),
    inference(superposition,[status(thm)],[c_126494,c_776]) ).

tcf(c_129029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X4),X5),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),tc_prod(X4,X4),X5),X4),X4) ),
    inference(superposition,[status(thm)],[c_126495,c_776]) ).

tcf(c_129030,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X4),X5),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X4),X5),X4),X4) ),
    inference(superposition,[status(thm)],[c_126540,c_776]) ).

tcf(c_129031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126781,c_776]) ).

tcf(c_129032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X4),X5),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),tc_prod(X4,X4),X5),X4),X4) ),
    inference(superposition,[status(thm)],[c_126547,c_776]) ).

tcf(c_129033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126558,c_776]) ).

tcf(c_129034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126256,c_776]) ).

tcf(c_129035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126286,c_776]) ).

tcf(c_129036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126246,c_776]) ).

tcf(c_129037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_125942,c_776]) ).

tcf(c_129038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126578,c_776]) ).

tcf(c_129039,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126785,c_776]) ).

tcf(c_129040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126584,c_776]) ).

tcf(c_129041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126659,c_776]) ).

tcf(c_129042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126665,c_776]) ).

tcf(c_129043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X4,X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X4,X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_125830,c_776]) ).

tcf(c_129044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_126672,c_776]) ).

tcf(c_129045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_126871,c_776]) ).

tcf(c_129046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126789,c_776]) ).

tcf(c_129047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126792,c_776]) ).

tcf(c_129048,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126796,c_776]) ).

tcf(c_129049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126834,c_776]) ).

tcf(c_129050,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_127183,c_776]) ).

tcf(c_129051,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_127225,c_776]) ).

tcf(c_129342,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126837,c_125973]) ).

tcf(c_129343,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126837,c_125887]) ).

tcf(c_129344,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126837,c_776]) ).

tcf(c_129345,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126837,c_762]) ).

tcf(c_129346,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126837,c_761]) ).

tcf(c_129347,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126837,c_774]) ).

tcf(c_129348,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126837,c_770]) ).

tcf(c_129349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126837,c_768]) ).

tcf(c_129350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126837,c_763]) ).

tcf(c_129369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126839,c_125973]) ).

tcf(c_129370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126839,c_125887]) ).

tcf(c_129371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126839,c_776]) ).

tcf(c_129372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126839,c_762]) ).

tcf(c_129373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126839,c_761]) ).

tcf(c_129374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126839,c_774]) ).

tcf(c_129375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126839,c_770]) ).

tcf(c_129376,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126839,c_768]) ).

tcf(c_129377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126839,c_763]) ).

tcf(c_129407,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_687,c_127800]) ).

tcf(c_129411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_127800,c_125973]) ).

tcf(c_129412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_127800,c_125887]) ).

tcf(c_129413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127800,c_776]) ).

tcf(c_129414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127800,c_762]) ).

tcf(c_129416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127800,c_774]) ).

tcf(c_129417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_127800,c_770]) ).

tcf(c_129418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127800,c_768]) ).

tcf(c_129419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X4,X1,X1),X3,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3,X1) ),
    inference(superposition,[status(thm)],[c_127800,c_763]) ).

tcf(c_129420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_127800,c_840]) ).

tcf(c_129441,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_596,c_127816]) ).

tcf(c_129445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_127816,c_125973]) ).

tcf(c_129446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X3)),
    inference(superposition,[status(thm)],[c_127816,c_125887]) ).

tcf(c_129447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127816,c_776]) ).

tcf(c_129448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127816,c_762]) ).

tcf(c_129450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127816,c_774]) ).

tcf(c_129451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_127816,c_770]) ).

tcf(c_129452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127816,c_768]) ).

tcf(c_129453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X4,X1,X1),X3,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3,X1) ),
    inference(superposition,[status(thm)],[c_127816,c_763]) ).

tcf(c_129454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_127816,c_840]) ).

tcf(c_129469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X3,X4),X5),
    inference(superposition,[status(thm)],[c_127941,c_841]) ).

tcf(c_129474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),
    inference(superposition,[status(thm)],[c_127959,c_841]) ).

tcf(c_129475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X2),X3)),
    inference(superposition,[status(thm)],[c_743,c_127979]) ).

tcf(c_129480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),
    inference(superposition,[status(thm)],[c_127979,c_841]) ).

tcf(c_129487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),
    inference(superposition,[status(thm)],[c_128002,c_841]) ).

tcf(c_129493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),
    inference(superposition,[status(thm)],[c_128026,c_841]) ).

tcf(c_129496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_128047,c_125973]) ).

tcf(c_129497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_128047,c_125887]) ).

tcf(c_129498,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_128047,c_776]) ).

tcf(c_129499,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_128047,c_762]) ).

tcf(c_129501,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_128047,c_774]) ).

tcf(c_129502,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_128047,c_770]) ).

tcf(c_129503,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_128047,c_768]) ).

tcf(c_129504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_128047,c_763]) ).

tcf(c_129535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_128082,c_125973]) ).

tcf(c_129536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_128082,c_125887]) ).

tcf(c_129537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_128082,c_776]) ).

tcf(c_129538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_128082,c_762]) ).

tcf(c_129540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_128082,c_774]) ).

tcf(c_129541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_128082,c_770]) ).

tcf(c_129542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_128082,c_768]) ).

tcf(c_129543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_128082,c_763]) ).

tcf(c_129557,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125584,c_841]) ).

tcf(c_129565,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X1)
      | ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_563,c_806]) ).

tcf(c_129566,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X1)
      | ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_566,c_806]) ).

tcf(c_129567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_806]) ).

tcf(c_129569,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126015,c_806]) ).

tcf(c_129570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126019,c_806]) ).

tcf(c_129571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126024,c_806]) ).

tcf(c_129572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126026,c_806]) ).

tcf(c_129573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126028,c_806]) ).

tcf(c_129574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126079,c_806]) ).

tcf(c_129575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126084,c_806]) ).

tcf(c_129577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126110,c_806]) ).

tcf(c_129578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126112,c_806]) ).

tcf(c_129579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126143,c_806]) ).

tcf(c_129580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126242,c_806]) ).

tcf(c_129581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126149,c_806]) ).

tcf(c_129582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126155,c_806]) ).

tcf(c_129583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126161,c_806]) ).

tcf(c_129585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126249,c_806]) ).

tcf(c_129586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126289,c_806]) ).

tcf(c_129587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126295,c_806]) ).

tcf(c_129588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126397,c_806]) ).

tcf(c_129589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126399,c_806]) ).

tcf(c_129591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126413,c_806]) ).

tcf(c_129592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126717,c_806]) ).

tcf(c_129593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126724,c_806]) ).

tcf(c_129594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126759,c_806]) ).

tcf(c_129595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126766,c_806]) ).

tcf(c_129596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126774,c_806]) ).

tcf(c_129597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126082,c_806]) ).

tcf(c_129598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126781,c_806]) ).

tcf(c_129599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126256,c_806]) ).

tcf(c_129600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126246,c_806]) ).

tcf(c_129601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126578,c_806]) ).

tcf(c_129602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126659,c_806]) ).

tcf(c_129603,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126789,c_806]) ).

tcf(c_129604,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126796,c_806]) ).

tcf(c_129605,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126837,c_806]) ).

tcf(c_129606,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_128047,c_806]) ).

tcf(c_129607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_806]) ).

tcf(c_129608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_806]) ).

tcf(c_129756,plain,
    ! [X0: $i,X1: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,iPr_def_12,iPr_def_11),X0,iPr_def_11,iPr_def_12),X1,iPr_def_13)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,iPr_def_11,iPr_def_12),iPr_def_12,iPr_def_11),iPr_def_12) ),
    inference(superposition,[status(thm)],[c_7266,c_567]) ).

tcf(c_129757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X1,tc_prod(X2,X3)),c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),tc_prod(X2,X3))
      | hBOOL(hAPP(X4,c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),X3,X2),X0,X2,X3)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_567,c_550]) ).

tcf(c_129758,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X2),X0,X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_125973]) ).

tcf(c_129759,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X2),X0,X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_125887]) ).

tcf(c_129760,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),c_Relation_ODomain(X1,X2,X2),X2)
      | ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = X0 )
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_806]) ).

tcf(c_129761,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_776]) ).

tcf(c_129762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X3,X2)
      | ~ c_Relation_Orefl__on(X3,X1,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_762]) ).

tcf(c_129763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X2),X3,X2)
      | ~ c_Relation_Orefl__on(X3,X1,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_761]) ).

tcf(c_129764,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_772]) ).

tcf(c_129765,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_635]) ).

tcf(c_129766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Relation_Oconverse(X1,X2,X3),X2,X3),X2,X3),X1,tc_prod(X2,X3))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_567,c_639]) ).

tcf(c_129767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_OImage(X1,X4,X2,X3),X3)
      | ~ c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),X4,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_567,c_774]) ).

tcf(c_129769,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),c_Relation_ODomain(X1,X2,X3),X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_567,c_768]) ).

tcf(c_129770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),X0,X2,X3),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),X0,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),X4,tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)))
      | ~ c_Relation_Orefl__on(X1,X4,tc_prod(X2,X3))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_567,c_763]) ).

tcf(c_129771,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X3,X2),X0,X2,X3)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_567,c_840]) ).

tcf(c_129772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,hAPP(X2,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Product__Type_OSigma(X1,X2,X3,X4),X4,X3)),X4)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Product__Type_OSigma(X1,X2,X3,X4),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_567,c_766]) ).

tcf(c_129773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Product__Type_OSigma(X1,X2,X3,X4),X4,X3),X1,X3)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Product__Type_OSigma(X1,X2,X3,X4),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_567,c_765]) ).

tcf(c_129819,plain,
    ! [X0: $i,X1: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,iPr_def_12,iPr_def_11),X0,iPr_def_11,iPr_def_12),X1,iPr_def_13)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,iPr_def_11,iPr_def_12),iPr_def_12,iPr_def_11),iPr_def_12) ),
    inference(superposition,[status(thm)],[c_7266,c_568]) ).

tcf(c_129820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X1,tc_prod(X2,X3)),c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),tc_prod(X2,X3))
      | hBOOL(hAPP(X4,c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),X3,X2),X0,X2,X3)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_568,c_550]) ).

tcf(c_129821,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X2),X0,X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_125973]) ).

tcf(c_129822,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X2),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X2),X0,X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_125887]) ).

tcf(c_129823,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),c_Relation_ODomain(X1,X2,X2),X2)
      | ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = X0 )
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_806]) ).

tcf(c_129824,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_776]) ).

tcf(c_129826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X2),X3,X2)
      | ~ c_Relation_Orefl__on(X3,X1,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_761]) ).

tcf(c_129827,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2),X1,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_772]) ).

tcf(c_129828,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_OId__on(X1,X2),X2,X2) = X0 )
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_635]) ).

tcf(c_129829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Relation_Oconverse(X1,X2,X3),X2,X3),X2,X3),X1,tc_prod(X2,X3))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_568,c_639]) ).

tcf(c_129830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_OImage(X1,X4,X2,X3),X3)
      | ~ c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),X4,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_568,c_774]) ).

tcf(c_129832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),c_Relation_ODomain(X1,X2,X3),X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_568,c_768]) ).

tcf(c_129833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),X0,X2,X3),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),X0,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),X4,tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)))
      | ~ c_Relation_Orefl__on(X1,X4,tc_prod(X2,X3))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_568,c_763]) ).

tcf(c_129834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X3,X2),X0,X2,X3)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_568,c_840]) ).

tcf(c_129835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,hAPP(X2,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Product__Type_OSigma(X1,X2,X3,X4),X4,X3)),X4)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Product__Type_OSigma(X1,X2,X3,X4),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_568,c_766]) ).

tcf(c_129836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Product__Type_OSigma(X1,X2,X3,X4),X4,X3),X1,X3)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Product__Type_OSigma(X1,X2,X3,X4),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_568,c_765]) ).

tcf(c_129879,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1),X2,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_563,c_796]) ).

tcf(c_129880,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1),X2,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_566,c_796]) ).

tcf(c_129881,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_796]) ).

tcf(c_129882,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_796]) ).

tcf(c_129883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_796]) ).

tcf(c_129884,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125928,c_796]) ).

tcf(c_129885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125931,c_796]) ).

tcf(c_129886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125935,c_796]) ).

tcf(c_129887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125797,c_796]) ).

tcf(c_129888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125747,c_796]) ).

tcf(c_129889,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_125794,c_796]) ).

tcf(c_129890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125796,c_796]) ).

tcf(c_129891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125799,c_796]) ).

tcf(c_129892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125939,c_796]) ).

tcf(c_129893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_125952,c_796]) ).

tcf(c_129894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126382,c_796]) ).

tcf(c_129895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126383,c_796]) ).

tcf(c_129896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126030,c_796]) ).

tcf(c_129897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126086,c_796]) ).

tcf(c_129898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126146,c_796]) ).

tcf(c_129899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126152,c_796]) ).

tcf(c_129900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126158,c_796]) ).

tcf(c_129901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126163,c_796]) ).

tcf(c_129902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126252,c_796]) ).

tcf(c_129903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126292,c_796]) ).

tcf(c_129904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126297,c_796]) ).

tcf(c_129905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_126409,c_796]) ).

tcf(c_129906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126714,c_796]) ).

tcf(c_129907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126720,c_796]) ).

tcf(c_129908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126755,c_796]) ).

tcf(c_129909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126762,c_796]) ).

tcf(c_129910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126770,c_796]) ).

tcf(c_129911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126777,c_796]) ).

tcf(c_129912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_125746,c_796]) ).

tcf(c_129915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126785,c_796]) ).

tcf(c_129918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126792,c_796]) ).

tcf(c_129919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126834,c_796]) ).

tcf(c_129920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126839,c_796]) ).

tcf(c_129921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_128082,c_796]) ).

tcf(c_129922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_796]) ).

tcf(c_129936,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_687,c_129420]) ).

tcf(c_129937,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_698,c_129420]) ).

tcf(c_129942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),
    inference(superposition,[status(thm)],[c_129420,c_841]) ).

tcf(c_129944,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X1,X1),X2)),
    inference(light_normalisation,[status(thm)],[c_129936,c_596]) ).

tcf(c_129945,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1,X1),X2)),
    inference(superposition,[status(thm)],[c_596,c_129454]) ).

tcf(c_129951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),
    inference(superposition,[status(thm)],[c_129454,c_841]) ).

tcf(c_129952,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X1,X1),X2)),
    inference(light_normalisation,[status(thm)],[c_129945,c_596]) ).

tcf(c_129953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X1)),
    inference(superposition,[status(thm)],[c_129469,c_125973]) ).

tcf(c_129954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X1)),
    inference(superposition,[status(thm)],[c_129469,c_125887]) ).

tcf(c_129955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X5,X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X5,X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_129469,c_776]) ).

tcf(c_129956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X6,X7),X4) ),
    inference(superposition,[status(thm)],[c_129469,c_762]) ).

tcf(c_129957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X6,X7),X4) ),
    inference(superposition,[status(thm)],[c_129469,c_761]) ).

tcf(c_129958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,X7,X8)),X7,X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129469,c_774]) ).

tcf(c_129959,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,X6,X7)),X6,X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_129469,c_770]) ).

tcf(c_129960,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,X6,X7)),X6,X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_129469,c_768]) ).

tcf(c_129961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_129469,c_763]) ).

tcf(c_129975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129474,c_125973]) ).

tcf(c_129976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129474,c_125887]) ).

tcf(c_129977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129474,c_776]) ).

tcf(c_129978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6) ),
    inference(superposition,[status(thm)],[c_129474,c_762]) ).

tcf(c_129980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129474,c_774]) ).

tcf(c_129981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_129474,c_770]) ).

tcf(c_129982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_129474,c_768]) ).

tcf(c_129983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_129474,c_763]) ).

tcf(c_129993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X3),X4),
    inference(superposition,[status(thm)],[c_743,c_129480]) ).

tcf(c_129996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129480,c_125973]) ).

tcf(c_129997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129480,c_125887]) ).

tcf(c_129998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129480,c_776]) ).

tcf(c_129999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6) ),
    inference(superposition,[status(thm)],[c_129480,c_762]) ).

tcf(c_130001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129480,c_774]) ).

tcf(c_130002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_129480,c_770]) ).

tcf(c_130003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_129480,c_768]) ).

tcf(c_130004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_129480,c_763]) ).

tcf(c_130018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129487,c_125973]) ).

tcf(c_130019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129487,c_125887]) ).

tcf(c_130020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129487,c_776]) ).

tcf(c_130021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6) ),
    inference(superposition,[status(thm)],[c_129487,c_762]) ).

tcf(c_130023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129487,c_774]) ).

tcf(c_130024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_129487,c_770]) ).

tcf(c_130025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_129487,c_768]) ).

tcf(c_130026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_129487,c_763]) ).

tcf(c_130096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129493,c_125973]) ).

tcf(c_130097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6)),
    inference(superposition,[status(thm)],[c_129493,c_125887]) ).

tcf(c_130098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129493,c_776]) ).

tcf(c_130099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6) ),
    inference(superposition,[status(thm)],[c_129493,c_762]) ).

tcf(c_130101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129493,c_774]) ).

tcf(c_130102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_129493,c_770]) ).

tcf(c_130103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_129493,c_768]) ).

tcf(c_130104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_129493,c_763]) ).

tcf(c_130114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_687,c_129942]) ).

tcf(c_130115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_698,c_129942]) ).

tcf(c_130118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_129942,c_125973]) ).

tcf(c_130119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_129942,c_125887]) ).

tcf(c_130120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_129942,c_776]) ).

tcf(c_130121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4) ),
    inference(superposition,[status(thm)],[c_129942,c_762]) ).

tcf(c_130123,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129942,c_774]) ).

tcf(c_130124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_129942,c_770]) ).

tcf(c_130125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4,X5),X4),
    inference(superposition,[status(thm)],[c_129942,c_768]) ).

tcf(c_130126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3,X4) ),
    inference(superposition,[status(thm)],[c_129942,c_763]) ).

tcf(c_130137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X3),
    inference(superposition,[status(thm)],[c_596,c_129951]) ).

tcf(c_130141,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_129951,c_125973]) ).

tcf(c_130142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4)),
    inference(superposition,[status(thm)],[c_129951,c_125887]) ).

tcf(c_130143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_129951,c_776]) ).

tcf(c_130144,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4) ),
    inference(superposition,[status(thm)],[c_129951,c_762]) ).

tcf(c_130146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_129951,c_774]) ).

tcf(c_130147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_129951,c_770]) ).

tcf(c_130148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4,X5),X4),
    inference(superposition,[status(thm)],[c_129951,c_768]) ).

tcf(c_130149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3,X4) ),
    inference(superposition,[status(thm)],[c_129951,c_763]) ).

tcf(c_130165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125585,c_841]) ).

tcf(c_130173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X2,X0,iPr_def_11,iPr_def_12),c_Product__Type_OSigma(X3,X1,iPr_def_11,iPr_def_12),iPr_def_13)
      | ~ c_in(X2,X3,iPr_def_11)
      | ~ c_in(X0,hAPP(X1,X2),iPr_def_12) ),
    inference(superposition,[status(thm)],[c_7266,c_778]) ).

tcf(c_130174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X4,X1,X3,X3),X3),c_Pair(X2,X0,X3,X3)))
      | ~ c_in(X2,X4,X3)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_125973]) ).

tcf(c_130175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Product__Type_OSigma(X4,X1,X3,X3),X3),c_Pair(X2,X0,X3,X3)))
      | ~ c_in(X2,X4,X3)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_125887]) ).

tcf(c_130176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,X3,X3),X3),X3)
      | ~ c_in(X4,X1,X3)
      | ~ c_in(X0,hAPP(X2,X4),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,X3,X3),X3),X3) ),
    inference(superposition,[status(thm)],[c_778,c_776]) ).

tcf(c_130177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X3)
      | ~ c_in(X5,X1,X3)
      | ~ c_in(X4,hAPP(X2,X5),X3)
      | ~ c_Relation_Orefl__on(X0,c_Product__Type_OSigma(X1,X2,X3,X3),X3) ),
    inference(superposition,[status(thm)],[c_778,c_762]) ).

tcf(c_130178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X3)
      | ~ c_in(X5,X1,X3)
      | ~ c_in(X4,hAPP(X2,X5),X3)
      | ~ c_Relation_Orefl__on(X0,c_Product__Type_OSigma(X1,X2,X3,X3),X3) ),
    inference(superposition,[status(thm)],[c_778,c_761]) ).

tcf(c_130179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Product__Type_OSigma(X4,X1,X5,X3),X6,X5,X3),X3)
      | ~ c_in(X2,X6,X5)
      | ~ c_in(X2,X4,X5)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_774]) ).

tcf(c_130180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Product__Type_OSigma(X4,X1,X5,X3),X5,X3),X3,X5),X3)
      | ~ c_in(X2,X4,X5)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_770]) ).

tcf(c_130181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Relation_ODomain(c_Product__Type_OSigma(X4,X1,X5,X3),X5,X3),X5)
      | ~ c_in(X2,X4,X5)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_768]) ).

tcf(c_130182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(X6,X5,X2,X3),c_Pair(X6,X5,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),X4,tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)))
      | ~ c_in(X6,X0,X2)
      | ~ c_in(X5,hAPP(X1,X6),X3)
      | ~ c_Relation_Orefl__on(c_Product__Type_OSigma(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_778,c_763]) ).

tcf(c_130183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Product__Type_OSigma(X4,X1,X5,X3),c_Pair(X2,X0,X5,X3)))
      | ~ c_in(X2,X4,X5)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_840]) ).

tcf(c_130230,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X0,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_563,c_809]) ).

tcf(c_130231,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X0,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_566,c_809]) ).

tcf(c_130232,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_809]) ).

tcf(c_130233,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_809]) ).

tcf(c_130274,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_809]) ).

tcf(c_130275,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_809]) ).

tcf(c_130301,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,iPr_def_13),X2),X1))
      | ~ hBOOL(hAPP(hAPP(iPr_def_14,X2),X0))
      | ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,iPr_def_13),X0),X1)) ),
    inference(superposition,[status(thm)],[c_7267,c_858]) ).

tcf(c_130302,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(hAPP(iPr_def_14,X2),X1))
      | ~ hBOOL(hAPP(hAPP(iPr_def_14,X2),X0))
      | ~ hBOOL(hAPP(hAPP(iPr_def_14,X0),X1)) ),
    inference(light_normalisation,[status(thm)],[c_130301,c_7267]) ).

tcf(c_130312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_List_Olist__all2(c_TypeRel_Owiden(X0,X2),c_Conform_Osko__Conform__Xconfs__conv__map__1__1(X0,X4,X1,X3,X2),X5,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(X0,X2),X4,X5,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_Conform_Oconf(X0,X1,X2),X3,X4,tc_Value_Oval,tc_Type_Oty) ),
    inference(superposition,[status(thm)],[c_569,c_861]) ).

tcf(c_130314,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_List_Olist__all2(c_TypeRel_Owiden(v_P,iPr_def_13),X2,X1,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(iPr_def_14,X2,X0,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(c_TypeRel_Owiden(v_P,iPr_def_13),X0,X1,tc_Type_Oty,tc_Type_Oty) ),
    inference(superposition,[status(thm)],[c_7267,c_861]) ).

tcf(c_130315,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_List_Olist__all2(iPr_def_14,X2,X1,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(iPr_def_14,X2,X0,tc_Type_Oty,tc_Type_Oty)
      | ~ c_List_Olist__all2(iPr_def_14,X0,X1,tc_Type_Oty,tc_Type_Oty) ),
    inference(light_normalisation,[status(thm)],[c_130314,c_7267]) ).

tcf(c_130323,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X0,X1),c_Pair(X2,X3,X4,X5)),X4,X5),X6),X2)),
    inference(superposition,[status(thm)],[c_97184,c_125973]) ).

tcf(c_130325,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X3,X0,X4,X4),X5,X6,X7)),X6,X7),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X3,X0,X4,X4),X5,X6,X7)),X6,X7),X4),X4) ),
    inference(superposition,[status(thm)],[c_97184,c_776]) ).

tcf(c_130326,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X3,X4,X5,X5),X6,X7,X8)),X7,X8),X5) ),
    inference(superposition,[status(thm)],[c_97184,c_762]) ).

tcf(c_130327,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X3,X4,X5,X5),X6,X7,X8)),X7,X8),X5) ),
    inference(superposition,[status(thm)],[c_97184,c_761]) ).

tcf(c_130328,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(c_Pair(X0,X3,X2,X6),X7,X8,X9)),X8,X9),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_97184,c_774]) ).

tcf(c_130329,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X3,X0,X4,X5),X6,X7,X8)),X7,X8),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_97184,c_770]) ).

tcf(c_130330,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X0,X3,X4,X5),X6,X7,X8)),X7,X8),X4,X5),X4),
    inference(superposition,[status(thm)],[c_97184,c_768]) ).

tcf(c_130331,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X2,X2,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X0,X1),c_Pair(X2,X3,X4,X5)),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_97184,c_763]) ).

tcf(c_130344,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X0)),
    inference(superposition,[status(thm)],[c_97186,c_125973]) ).

tcf(c_130346,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X6),X4,X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X6),X4,X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_97186,c_776]) ).

tcf(c_130347,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X7),X5,X6),X3) ),
    inference(superposition,[status(thm)],[c_97186,c_762]) ).

tcf(c_130348,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X7),X5,X6),X3) ),
    inference(superposition,[status(thm)],[c_97186,c_761]) ).

tcf(c_130349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X4),X5,X6,X7)),X8),X6,X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_97186,c_774]) ).

tcf(c_130350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X3),X4,X5,X6)),X7),X5,X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_97186,c_770]) ).

tcf(c_130351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X3),X4,X5,X6)),X7),X5,X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_97186,c_768]) ).

tcf(c_130352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5,X6) ),
    inference(superposition,[status(thm)],[c_97186,c_763]) ).

tcf(c_130383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X0)),
    inference(superposition,[status(thm)],[c_97187,c_125973]) ).

tcf(c_130385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X6),X4,X5),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X6),X4,X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_97187,c_776]) ).

tcf(c_130386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X7),X5,X6),X3) ),
    inference(superposition,[status(thm)],[c_97187,c_762]) ).

tcf(c_130387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X7),X5,X6),X3) ),
    inference(superposition,[status(thm)],[c_97187,c_761]) ).

tcf(c_130388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X4),X5,X6,X7)),X8),X6,X7),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_97187,c_774]) ).

tcf(c_130389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X3),X4,X5,X6)),X7),X5,X6),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_97187,c_770]) ).

tcf(c_130390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X3),X4,X5,X6)),X7),X5,X6),X2,X3),X2),
    inference(superposition,[status(thm)],[c_97187,c_768]) ).

tcf(c_130391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5,X6) ),
    inference(superposition,[status(thm)],[c_97187,c_763]) ).

tcf(c_130405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_97192,c_125973]) ).

tcf(c_130407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_97192,c_776]) ).

tcf(c_130408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_97192,c_762]) ).

tcf(c_130410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_97192,c_774]) ).

tcf(c_130411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_97192,c_770]) ).

tcf(c_130412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_97192,c_768]) ).

tcf(c_130413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_97192,c_763]) ).

tcf(c_130427,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X2),X0))
      | ~ c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_125571]) ).

tcf(c_130428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),X3))
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),X2),X0,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_125571,c_517]) ).

tcf(c_130429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),X4))
      | ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),X2,X3),X0,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_125571,c_537]) ).

tcf(c_130430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X3)
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125571,c_841]) ).

tcf(c_130441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_125943,c_841]) ).

tcf(c_130446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_125947,c_841]) ).

tcf(c_130451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126006,c_841]) ).

tcf(c_130457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126009,c_841]) ).

tcf(c_130460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125586,c_841]) ).

tcf(c_130470,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_563,c_561]) ).

tcf(c_130471,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_566,c_561]) ).

tcf(c_130472,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),X1,t_a,t_a)))
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_567,c_561]) ).

tcf(c_130473,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),X1,t_a,t_a)))
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_568,c_561]) ).

tcf(c_130474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Otrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_603,c_561]) ).

tcf(c_130475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,X2))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_Oconverse(X1,t_a,t_a)),X2,t_a,t_a),X1,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_641,c_561]) ).

tcf(c_130476,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a))))
      | ~ c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X1,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a)),X1,t_a) ),
    inference(superposition,[status(thm)],[c_771,c_561]) ).

tcf(c_130477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,X3))
      | ~ c_in(X3,X1,t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,t_a,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Product__Type_OSigma(X1,X2,t_a,t_a)),hAPP(X2,X3),t_a) ),
    inference(superposition,[status(thm)],[c_778,c_561]) ).

tcf(c_130478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_844,c_561]) ).

tcf(c_130479,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X2,c_Transitive__Closure_Ortrancl(X1,t_a))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,t_a),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125781,c_561]) ).

tcf(c_130480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125794,c_561]) ).

tcf(c_130481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125952,c_561]) ).

tcf(c_130482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126107,c_561]) ).

tcf(c_130483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126394,c_561]) ).

tcf(c_130484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126404,c_561]) ).

tcf(c_130485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126409,c_561]) ).

tcf(c_130486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X4))
      | hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125711,c_561]) ).

tcf(c_130487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126082,c_561]) ).

tcf(c_130488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125746,c_561]) ).

tcf(c_130489,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126528,c_561]) ).

tcf(c_130490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126533,c_561]) ).

tcf(c_130491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126558,c_561]) ).

tcf(c_130492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126256,c_561]) ).

tcf(c_130493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126286,c_561]) ).

tcf(c_130494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126246,c_561]) ).

tcf(c_130495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125942,c_561]) ).

tcf(c_130496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126578,c_561]) ).

tcf(c_130497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126584,c_561]) ).

tcf(c_130498,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126659,c_561]) ).

tcf(c_130499,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126665,c_561]) ).

tcf(c_130500,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126672,c_561]) ).

tcf(c_130501,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126871,c_561]) ).

tcf(c_130502,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127183,c_561]) ).

tcf(c_130503,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127225,c_561]) ).

tcf(c_130504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_128047,c_561]) ).

tcf(c_130505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_128082,c_561]) ).

tcf(c_130506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129474,c_561]) ).

tcf(c_130507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129480,c_561]) ).

tcf(c_130508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129487,c_561]) ).

tcf(c_130509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129493,c_561]) ).

tcf(c_130510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129942,c_561]) ).

tcf(c_130511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129951,c_561]) ).

tcf(c_130512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_97192,c_561]) ).

tcf(c_130698,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_563,c_564]) ).

tcf(c_130699,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_566,c_564]) ).

tcf(c_130700,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),X1,t_a,t_a)))
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_567,c_564]) ).

tcf(c_130701,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),X1,t_a,t_a)))
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_568,c_564]) ).

tcf(c_130702,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Otrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_603,c_564]) ).

tcf(c_130703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,X2))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_Oconverse(X1,t_a,t_a)),X2,t_a,t_a),X1,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_641,c_564]) ).

tcf(c_130704,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_OId__on(X1,t_a))))
      | ~ c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X1,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_OId__on(X1,t_a)),X1,t_a) ),
    inference(superposition,[status(thm)],[c_771,c_564]) ).

tcf(c_130705,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,X3))
      | ~ c_in(X3,X1,t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,t_a,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Product__Type_OSigma(X1,X2,t_a,t_a)),hAPP(X2,X3),t_a) ),
    inference(superposition,[status(thm)],[c_778,c_564]) ).

tcf(c_130706,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_844,c_564]) ).

tcf(c_130707,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X2,c_Transitive__Closure_Ortrancl(X1,t_a))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,t_a),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125781,c_564]) ).

tcf(c_130708,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125794,c_564]) ).

tcf(c_130709,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125952,c_564]) ).

tcf(c_130710,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126107,c_564]) ).

tcf(c_130711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126394,c_564]) ).

tcf(c_130712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126404,c_564]) ).

tcf(c_130713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126409,c_564]) ).

tcf(c_130803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_596,c_790]) ).

tcf(c_130805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_684,c_790]) ).

tcf(c_130806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_687,c_790]) ).

tcf(c_130807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,X2))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a)),X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_790,c_564]) ).

tcf(c_130808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,X2))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a)),X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_790,c_561]) ).

tcf(c_130809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),c_Pair(X1,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_125973]) ).

tcf(c_130810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),c_Pair(X1,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_125887]) ).

tcf(c_130811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X2,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_809]) ).

tcf(c_130812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X3,X2,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_806]) ).

tcf(c_130813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_776]) ).

tcf(c_130814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_762]) ).

tcf(c_130815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_761]) ).

tcf(c_130816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X4,X2,X2),X2)
      | ~ c_in(X1,X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_774]) ).

tcf(c_130817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_770]) ).

tcf(c_130818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_768]) ).

tcf(c_130819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X1,X0,X2,X2),c_Pair(X1,X0,X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X4,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_763]) ).

tcf(c_130820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),c_Pair(X1,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_840]) ).

tcf(c_130887,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X0,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_791]) ).

tcf(c_130888,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X0,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_791]) ).

tcf(c_130889,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_791]) ).

tcf(c_130890,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_791]) ).

tcf(c_130892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_791]) ).

tcf(c_130894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_596,c_791]) ).

tcf(c_130897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_687,c_791]) ).

tcf(c_130912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),
    inference(superposition,[status(thm)],[c_126010,c_841]) ).

tcf(c_130915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126299,c_841]) ).

tcf(c_130918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126300,c_841]) ).

tcf(c_130925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126305,c_841]) ).

tcf(c_130932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126306,c_841]) ).

tcf(c_130936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126310,c_841]) ).

tcf(c_130940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126311,c_841]) ).

tcf(c_130944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126315,c_841]) ).

tcf(c_130947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126316,c_841]) ).

tcf(c_130960,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126321,c_841]) ).

tcf(c_130967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126322,c_841]) ).

tcf(c_130974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126327,c_841]) ).

tcf(c_130979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125587,c_841]) ).

tcf(c_131001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X1,X2),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_563,c_565]) ).

tcf(c_131002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X1,X2),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_566,c_565]) ).

tcf(c_131003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,X2),X1,X2,X2)))
      | ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,X2),c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_565]) ).

tcf(c_131004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,X2),X1,X2,X2)))
      | ~ c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,X1,X2),c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_565]) ).

tcf(c_131005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,X3),X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Transitive__Closure_Otrancl(X2,X3),X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_603,c_565]) ).

tcf(c_131006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,X3))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_Oconverse(X1,X2,X2),X2),X3,X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_565]) ).

tcf(c_131007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_OId__on(X1,X2),X2)))
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_OId__on(X1,X2),X2),X1,X2) ),
    inference(superposition,[status(thm)],[c_771,c_565]) ).

tcf(c_131008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X0,X4))
      | ~ c_in(X4,X1,X3)
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,X3,X3),X3),X3)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Product__Type_OSigma(X1,X2,X3,X3),X3),hAPP(X2,X4),X3) ),
    inference(superposition,[status(thm)],[c_778,c_565]) ).

tcf(c_131009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,X3))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_565]) ).

tcf(c_131010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_844,c_565]) ).

tcf(c_131011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,c_Transitive__Closure_Ortrancl(X1,X2),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_125781,c_565]) ).

tcf(c_131012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2),X2) ),
    inference(superposition,[status(thm)],[c_125794,c_565]) ).

tcf(c_131013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_125952,c_565]) ).

tcf(c_131014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2),X2) ),
    inference(superposition,[status(thm)],[c_126107,c_565]) ).

tcf(c_131015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_126394,c_565]) ).

tcf(c_131016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_126404,c_565]) ).

tcf(c_131017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2),X2) ),
    inference(superposition,[status(thm)],[c_126409,c_565]) ).

tcf(c_131018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_125711,c_565]) ).

tcf(c_131019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_126082,c_565]) ).

tcf(c_131020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_125746,c_565]) ).

tcf(c_131021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_126528,c_565]) ).

tcf(c_131022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_126533,c_565]) ).

tcf(c_131023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126558,c_565]) ).

tcf(c_131024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126256,c_565]) ).

tcf(c_131025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126286,c_565]) ).

tcf(c_131026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126246,c_565]) ).

tcf(c_131027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_125942,c_565]) ).

tcf(c_131028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126578,c_565]) ).

tcf(c_131029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126584,c_565]) ).

tcf(c_131030,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126659,c_565]) ).

tcf(c_131031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_126665,c_565]) ).

tcf(c_131032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_126672,c_565]) ).

tcf(c_131033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_126871,c_565]) ).

tcf(c_131034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_127183,c_565]) ).

tcf(c_131035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_127225,c_565]) ).

tcf(c_131036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_128047,c_565]) ).

tcf(c_131037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_128082,c_565]) ).

tcf(c_131038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129474,c_565]) ).

tcf(c_131039,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129480,c_565]) ).

tcf(c_131040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129487,c_565]) ).

tcf(c_131041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_129493,c_565]) ).

tcf(c_131042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_129942,c_565]) ).

tcf(c_131043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_129951,c_565]) ).

tcf(c_131044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_97192,c_565]) ).

tcf(c_131251,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),X2,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_563,c_789]) ).

tcf(c_131252,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),X2,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1) = X2 ) ),
    inference(superposition,[status(thm)],[c_566,c_789]) ).

tcf(c_131253,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X0,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = X0 )
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_789]) ).

tcf(c_131254,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X0,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = X0 )
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_789]) ).

tcf(c_131255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_789]) ).

tcf(c_131256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_789]) ).

tcf(c_131258,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126015,c_789]) ).

tcf(c_131259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126019,c_789]) ).

tcf(c_131260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126024,c_789]) ).

tcf(c_131261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126026,c_789]) ).

tcf(c_131262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126028,c_789]) ).

tcf(c_131263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126079,c_789]) ).

tcf(c_131264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126084,c_789]) ).

tcf(c_131266,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126110,c_789]) ).

tcf(c_131267,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126112,c_789]) ).

tcf(c_131268,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126143,c_789]) ).

tcf(c_131269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126242,c_789]) ).

tcf(c_131270,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126149,c_789]) ).

tcf(c_131271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126155,c_789]) ).

tcf(c_131272,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126161,c_789]) ).

tcf(c_131274,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126249,c_789]) ).

tcf(c_131275,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126289,c_789]) ).

tcf(c_131276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126295,c_789]) ).

tcf(c_131277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126397,c_789]) ).

tcf(c_131278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126399,c_789]) ).

tcf(c_131280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126413,c_789]) ).

tcf(c_131281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126717,c_789]) ).

tcf(c_131282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126724,c_789]) ).

tcf(c_131283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126759,c_789]) ).

tcf(c_131284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126766,c_789]) ).

tcf(c_131285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126774,c_789]) ).

tcf(c_131286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126082,c_789]) ).

tcf(c_131287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126781,c_789]) ).

tcf(c_131292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126789,c_789]) ).

tcf(c_131293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126796,c_789]) ).

tcf(c_131294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_126837,c_789]) ).

tcf(c_131295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_128047,c_789]) ).

tcf(c_131296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_789]) ).

tcf(c_131297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_789]) ).

tcf(c_131327,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126328,c_841]) ).

tcf(c_131331,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126332,c_841]) ).

tcf(c_131335,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126333,c_841]) ).

tcf(c_131349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId__on(X1,X2),X3)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126352,c_841]) ).

tcf(c_131357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126369,c_841]) ).

tcf(c_131379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126370,c_841]) ).

tcf(c_131383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126374,c_841]) ).

tcf(c_131387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126375,c_841]) ).

tcf(c_131390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126378,c_841]) ).

tcf(c_131392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126379,c_841]) ).

tcf(c_131396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125588,c_841]) ).

tcf(c_131406,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_563,c_560]) ).

tcf(c_131407,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X2,X1),t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_566,c_560]) ).

tcf(c_131408,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),X1,t_a,t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_567,c_560]) ).

tcf(c_131409,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),X1,t_a,t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_568,c_560]) ).

tcf(c_131410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Otrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_603,c_560]) ).

tcf(c_131411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_Oconverse(X1,t_a,t_a)),X2,t_a,t_a),X1,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_641,c_560]) ).

tcf(c_131412,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_OId__on(X1,t_a)),c_Wellfounded_Oacc(c_Relation_OId__on(X1,t_a),t_a),t_a)
      | ~ c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X1,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Relation_OId__on(X1,t_a)),X1,t_a) ),
    inference(superposition,[status(thm)],[c_771,c_560]) ).

tcf(c_131413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(X3,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,t_a,t_a),t_a),t_a)
      | ~ c_in(X3,X1,t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,t_a,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Product__Type_OSigma(X1,X2,t_a,t_a)),hAPP(X2,X3),t_a) ),
    inference(superposition,[status(thm)],[c_778,c_560]) ).

tcf(c_131414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinduct__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a)),X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_790,c_560]) ).

tcf(c_131415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_844,c_560]) ).

tcf(c_131416,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X2,c_Transitive__Closure_Ortrancl(X1,t_a)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,t_a),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,t_a),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125781,c_560]) ).

tcf(c_131417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125794,c_560]) ).

tcf(c_131418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125952,c_560]) ).

tcf(c_131419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126107,c_560]) ).

tcf(c_131420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126394,c_560]) ).

tcf(c_131421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126404,c_560]) ).

tcf(c_131422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126409,c_560]) ).

tcf(c_131423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125711,c_560]) ).

tcf(c_131424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126082,c_560]) ).

tcf(c_131425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125746,c_560]) ).

tcf(c_131426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126528,c_560]) ).

tcf(c_131427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126533,c_560]) ).

tcf(c_131428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126558,c_560]) ).

tcf(c_131429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126256,c_560]) ).

tcf(c_131430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126286,c_560]) ).

tcf(c_131431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126246,c_560]) ).

tcf(c_131432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125942,c_560]) ).

tcf(c_131433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126578,c_560]) ).

tcf(c_131434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126584,c_560]) ).

tcf(c_131435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126659,c_560]) ).

tcf(c_131436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126665,c_560]) ).

tcf(c_131437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126672,c_560]) ).

tcf(c_131438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126871,c_560]) ).

tcf(c_131439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127183,c_560]) ).

tcf(c_131440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127225,c_560]) ).

tcf(c_131441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_128047,c_560]) ).

tcf(c_131442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_128082,c_560]) ).

tcf(c_131443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129474,c_560]) ).

tcf(c_131444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129480,c_560]) ).

tcf(c_131445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129487,c_560]) ).

tcf(c_131446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129493,c_560]) ).

tcf(c_131447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129942,c_560]) ).

tcf(c_131448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_129951,c_560]) ).

tcf(c_131449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_97192,c_560]) ).

tcf(c_131775,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_563,c_562]) ).

tcf(c_131776,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),c_Wellfounded_Oacc(X1,t_a),t_a)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X2,X1),t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_566,c_562]) ).

tcf(c_131777,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),X1,t_a,t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_567,c_562]) ).

tcf(c_131778,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),X1,t_a,t_a),c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1),c_Relation_ODomain(c_Relation_Oconverse(X1,t_a,t_a),t_a,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_568,c_562]) ).

tcf(c_131779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Otrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_603,c_562]) ).

tcf(c_131780,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_Oconverse(X1,t_a,t_a)),X2,t_a,t_a),X1,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_641,c_562]) ).

tcf(c_131781,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a)),c_Wellfounded_Oacc(c_Relation_OId__on(X1,t_a),t_a),t_a)
      | ~ c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X1,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a)),X1,t_a) ),
    inference(superposition,[status(thm)],[c_771,c_562]) ).

tcf(c_131782,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(X3,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,t_a,t_a),t_a),t_a)
      | ~ c_in(X3,X1,t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Product__Type_OSigma(X1,X2,t_a,t_a),t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Product__Type_OSigma(X1,X2,t_a,t_a)),hAPP(X2,X3),t_a) ),
    inference(superposition,[status(thm)],[c_778,c_562]) ).

tcf(c_131783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a),t_a),t_a)
      | ~ c_in(c_Pair(v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,t_a,t_a),t_a)),X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_790,c_562]) ).

tcf(c_131784,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_844,c_562]) ).

tcf(c_131785,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X2,c_Transitive__Closure_Ortrancl(X1,t_a)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,t_a),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,t_a),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125781,c_562]) ).

tcf(c_131786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125794,c_562]) ).

tcf(c_131787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_125952,c_562]) ).

tcf(c_131788,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126107,c_562]) ).

tcf(c_131789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126394,c_562]) ).

tcf(c_131790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126404,c_562]) ).

tcf(c_131791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126409,c_562]) ).

tcf(c_131887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X2,tc_prod(t_a,t_a)),c_Wellfounded_Oacc(X2,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | hBOOL(hAPP(X3,c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Wellfounded_Oacc(X2,tc_prod(t_a,t_a))),X1,t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(X2,tc_prod(t_a,t_a)),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_550]) ).

tcf(c_131888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),X2),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_560]) ).

tcf(c_131889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),X2)))
      | ( v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_564]) ).

tcf(c_131890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),X2),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_562]) ).

tcf(c_131891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),X2)))
      | ( v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_561]) ).

tcf(c_131892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,t_a),X2)))
      | ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,t_a) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_565]) ).

tcf(c_131893,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X2,t_a),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_125973]) ).

tcf(c_131894,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X2,t_a),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_125887]) ).

tcf(c_131895,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X1,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)) = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_789]) ).

tcf(c_131896,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_809]) ).

tcf(c_131897,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),c_Relation_ODomain(X2,t_a,t_a),t_a)
      | ( X0 = X1 )
      | ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)) = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_806]) ).

tcf(c_131898,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_776]) ).

tcf(c_131899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,X3,t_a)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X3,X2,t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_762]) ).

tcf(c_131900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X3,X2,t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_761]) ).

tcf(c_131901,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Otrancl(X2,t_a)),X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_796]) ).

tcf(c_131902,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Relation_OId__on(X2,t_a)),X2,t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_772]) ).

tcf(c_131903,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X1 )
      | ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Relation_OId__on(X2,t_a)) = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_635]) ).

tcf(c_131904,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Relation_Oconverse(X2,t_a,t_a)),t_a,t_a),X2,tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,t_a,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_639]) ).

tcf(c_131905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_OImage(X2,X3,t_a,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_774]) ).

tcf(c_131906,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X2,t_a,t_a),t_a,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_770]) ).

tcf(c_131907,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),c_Relation_ODomain(X2,t_a,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_768]) ).

tcf(c_131908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),X3,tc_prod(tc_prod(t_a,t_a),tc_prod(t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X2,X3,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_763]) ).

tcf(c_131909,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X2,c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_840]) ).

tcf(c_131910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Product__Type_OSigma(X2,X3,t_a,t_a))),t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X2,X3,t_a,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_766]) ).

tcf(c_131911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Product__Type_OSigma(X2,X3,t_a,t_a)),X2,t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X2,X3,t_a,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_765]) ).

tcf(c_131912,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,t_a,t_a),t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,t_a,t_a),t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_791]) ).

tcf(c_132143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2)))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2))) ),
    inference(superposition,[status(thm)],[c_563,c_786]) ).

tcf(c_132144,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2)))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2))) ),
    inference(superposition,[status(thm)],[c_566,c_786]) ).

tcf(c_132145,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2)))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_786]) ).

tcf(c_132146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2)))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_786]) ).

tcf(c_132147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X1))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X2,t_a)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_786]) ).

tcf(c_132148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X1,c_Relation_Oconverse(X3,X2,X2),X2)))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_786]) ).

tcf(c_132149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2)))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_786]) ).

tcf(c_132151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126015,c_786]) ).

tcf(c_132152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126019,c_786]) ).

tcf(c_132153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126024,c_786]) ).

tcf(c_132154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126026,c_786]) ).

tcf(c_132155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126028,c_786]) ).

tcf(c_132156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126079,c_786]) ).

tcf(c_132157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126084,c_786]) ).

tcf(c_132159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126110,c_786]) ).

tcf(c_132160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126112,c_786]) ).

tcf(c_132161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126143,c_786]) ).

tcf(c_132162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126242,c_786]) ).

tcf(c_132163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126149,c_786]) ).

tcf(c_132164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126155,c_786]) ).

tcf(c_132165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126161,c_786]) ).

tcf(c_132167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126249,c_786]) ).

tcf(c_132168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126289,c_786]) ).

tcf(c_132169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126295,c_786]) ).

tcf(c_132170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126397,c_786]) ).

tcf(c_132171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126399,c_786]) ).

tcf(c_132173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126413,c_786]) ).

tcf(c_132174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126717,c_786]) ).

tcf(c_132175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126724,c_786]) ).

tcf(c_132176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126759,c_786]) ).

tcf(c_132177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126766,c_786]) ).

tcf(c_132178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126774,c_786]) ).

tcf(c_132179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126082,c_786]) ).

tcf(c_132180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126781,c_786]) ).

tcf(c_132181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126256,c_786]) ).

tcf(c_132182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126246,c_786]) ).

tcf(c_132183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126578,c_786]) ).

tcf(c_132184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126659,c_786]) ).

tcf(c_132185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126789,c_786]) ).

tcf(c_132186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126796,c_786]) ).

tcf(c_132187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126837,c_786]) ).

tcf(c_132188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_128047,c_786]) ).

tcf(c_132189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,c_Transitive__Closure_Otrancl(X3,X2),X2)))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_786]) ).

tcf(c_132190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_786]) ).

tcf(c_132388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126585,c_125973]) ).

tcf(c_132389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_126585,c_125887]) ).

tcf(c_132390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X4,X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X4,X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_126585,c_776]) ).

tcf(c_132391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126585,c_762]) ).

tcf(c_132392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_126585,c_761]) ).

tcf(c_132393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X2),X3,X4,X5)),X4,X5),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_126585,c_796]) ).

tcf(c_132394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X4),X5,X6,X7)),X6,X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126585,c_774]) ).

tcf(c_132395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X3),X4,X5,X6)),X5,X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_126585,c_770]) ).

tcf(c_132396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X3),X4,X5,X6)),X5,X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_126585,c_768]) ).

tcf(c_132397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_126585,c_763]) ).

tcf(c_132430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126677,c_841]) ).

tcf(c_132438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126678,c_841]) ).

tcf(c_132446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126685,c_841]) ).

tcf(c_132453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126686,c_841]) ).

tcf(c_132465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126692,c_841]) ).

tcf(c_132486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126693,c_841]) ).

tcf(c_132493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126699,c_841]) ).

tcf(c_132499,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126700,c_841]) ).

tcf(c_132506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_126707,c_841]) ).

tcf(c_132511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),X2),X7),
    inference(superposition,[status(thm)],[c_125589,c_841]) ).

tcf(c_132521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3)))
      | c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_563,c_800]) ).

tcf(c_132522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3)))
      | c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_566,c_800]) ).

tcf(c_132523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X0,X1,X2)))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_800]) ).

tcf(c_132524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X0,X1,X2)))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_800]) ).

tcf(c_132525,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X1,X2,t_a)))
      | hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X1))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_800]) ).

tcf(c_132526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X0,c_Relation_Oconverse(X3,X2,X2),X2)))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_800]) ).

tcf(c_132527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2)))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_800]) ).

tcf(c_132529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126015,c_800]) ).

tcf(c_132530,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126019,c_800]) ).

tcf(c_132531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126024,c_800]) ).

tcf(c_132532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126026,c_800]) ).

tcf(c_132533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126028,c_800]) ).

tcf(c_132534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126079,c_800]) ).

tcf(c_132535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126084,c_800]) ).

tcf(c_132537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126110,c_800]) ).

tcf(c_132538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126112,c_800]) ).

tcf(c_132539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126143,c_800]) ).

tcf(c_132540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126242,c_800]) ).

tcf(c_132541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126149,c_800]) ).

tcf(c_132542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126155,c_800]) ).

tcf(c_132543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126161,c_800]) ).

tcf(c_132545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126249,c_800]) ).

tcf(c_132546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126289,c_800]) ).

tcf(c_132547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126295,c_800]) ).

tcf(c_132548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126397,c_800]) ).

tcf(c_132549,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126399,c_800]) ).

tcf(c_132551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126413,c_800]) ).

tcf(c_132552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126717,c_800]) ).

tcf(c_132553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126724,c_800]) ).

tcf(c_132554,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126759,c_800]) ).

tcf(c_132555,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126766,c_800]) ).

tcf(c_132556,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126774,c_800]) ).

tcf(c_132557,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126082,c_800]) ).

tcf(c_132558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126781,c_800]) ).

tcf(c_132559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126256,c_800]) ).

tcf(c_132560,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126246,c_800]) ).

tcf(c_132561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126578,c_800]) ).

tcf(c_132562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126659,c_800]) ).

tcf(c_132563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126789,c_800]) ).

tcf(c_132564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126796,c_800]) ).

tcf(c_132565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126837,c_800]) ).

tcf(c_132566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_128047,c_800]) ).

tcf(c_132567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,c_Transitive__Closure_Otrancl(X3,X2),X2)))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_800]) ).

tcf(c_132568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_800]) ).

tcf(c_132800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | ( X1 = X3 )
      | ~ c_Relation_Osingle__valued(X0,X2,X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),X3,X2,X2),X0,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_642]) ).

tcf(c_132801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | ( X1 = X3 )
      | ~ c_Relation_Osingle__valued(X0,X2,X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X3,X2,X2),X0,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_642]) ).

tcf(c_132802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X4 )
      | ~ c_Relation_Osingle__valued(X1,X3,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X2),X2,X3),X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X3),X4,X3,X2),X1,tc_prod(X3,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_642]) ).

tcf(c_132803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X4 )
      | ~ c_Relation_Osingle__valued(X1,X3,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X2),X2,X3),X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X3),X4,X3,X2),X1,tc_prod(X3,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_642]) ).

tcf(c_132804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_642]) ).

tcf(c_132805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X4,X3,X2),X2,X3)
      | ~ c_in(c_Pair(X5,X0,X3,X2),X4,tc_prod(X3,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_641,c_642]) ).

tcf(c_132806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ~ c_in(X0,X3,X2)
      | ~ c_Relation_Osingle__valued(c_Relation_OId__on(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_771,c_642]) ).

tcf(c_132807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X6 )
      | ~ c_in(X0,X4,X2)
      | ~ c_in(X6,hAPP(X5,X0),X3)
      | ~ c_Relation_Osingle__valued(c_Product__Type_OSigma(X4,X5,X2,X3),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Product__Type_OSigma(X4,X5,X2,X3),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_778,c_642]) ).

tcf(c_132808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X2,t_a,t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_642]) ).

tcf(c_132809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2,X2)
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_642]) ).

tcf(c_132810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_642]) ).

tcf(c_132811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125697,c_642]) ).

tcf(c_132812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125698,c_642]) ).

tcf(c_132813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125699,c_642]) ).

tcf(c_132814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125781,c_642]) ).

tcf(c_132815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125928,c_642]) ).

tcf(c_132816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125931,c_642]) ).

tcf(c_132817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125935,c_642]) ).

tcf(c_132818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125797,c_642]) ).

tcf(c_132819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125747,c_642]) ).

tcf(c_132820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125794,c_642]) ).

tcf(c_132821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125796,c_642]) ).

tcf(c_132822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125799,c_642]) ).

tcf(c_132823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125939,c_642]) ).

tcf(c_132824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125952,c_642]) ).

tcf(c_132825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126382,c_642]) ).

tcf(c_132826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126383,c_642]) ).

tcf(c_132827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126015,c_642]) ).

tcf(c_132828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126019,c_642]) ).

tcf(c_132829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126024,c_642]) ).

tcf(c_132830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126026,c_642]) ).

tcf(c_132831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126028,c_642]) ).

tcf(c_132832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126030,c_642]) ).

tcf(c_132833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126079,c_642]) ).

tcf(c_132834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126084,c_642]) ).

tcf(c_132835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126086,c_642]) ).

tcf(c_132836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126107,c_642]) ).

tcf(c_132837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126110,c_642]) ).

tcf(c_132838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126112,c_642]) ).

tcf(c_132839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126143,c_642]) ).

tcf(c_132840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126146,c_642]) ).

tcf(c_132841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126242,c_642]) ).

tcf(c_132842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126149,c_642]) ).

tcf(c_132843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126152,c_642]) ).

tcf(c_132844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126155,c_642]) ).

tcf(c_132845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126158,c_642]) ).

tcf(c_132846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126161,c_642]) ).

tcf(c_132847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126163,c_642]) ).

tcf(c_132848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126394,c_642]) ).

tcf(c_132849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126249,c_642]) ).

tcf(c_132850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126252,c_642]) ).

tcf(c_132851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126289,c_642]) ).

tcf(c_132852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126292,c_642]) ).

tcf(c_132853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126295,c_642]) ).

tcf(c_132854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126297,c_642]) ).

tcf(c_132855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126397,c_642]) ).

tcf(c_132856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126399,c_642]) ).

tcf(c_132857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126404,c_642]) ).

tcf(c_132858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126409,c_642]) ).

tcf(c_132859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126413,c_642]) ).

tcf(c_132860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126714,c_642]) ).

tcf(c_132861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126717,c_642]) ).

tcf(c_132862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126720,c_642]) ).

tcf(c_132863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126724,c_642]) ).

tcf(c_132864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126755,c_642]) ).

tcf(c_132865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126759,c_642]) ).

tcf(c_132866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126762,c_642]) ).

tcf(c_132867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126766,c_642]) ).

tcf(c_132868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126770,c_642]) ).

tcf(c_132869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126774,c_642]) ).

tcf(c_132870,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126777,c_642]) ).

tcf(c_132871,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125711,c_642]) ).

tcf(c_132872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126082,c_642]) ).

tcf(c_132873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125746,c_642]) ).

tcf(c_132874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126528,c_642]) ).

tcf(c_132875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126533,c_642]) ).

tcf(c_132876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126781,c_642]) ).

tcf(c_132877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126558,c_642]) ).

tcf(c_132878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126256,c_642]) ).

tcf(c_132879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126286,c_642]) ).

tcf(c_132880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126246,c_642]) ).

tcf(c_132881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125942,c_642]) ).

tcf(c_132882,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126578,c_642]) ).

tcf(c_132883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126785,c_642]) ).

tcf(c_132884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126584,c_642]) ).

tcf(c_132885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126659,c_642]) ).

tcf(c_132886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126665,c_642]) ).

tcf(c_132887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X6,X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X6,X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_125830,c_642]) ).

tcf(c_132888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126672,c_642]) ).

tcf(c_132889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126871,c_642]) ).

tcf(c_132890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126789,c_642]) ).

tcf(c_132891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126792,c_642]) ).

tcf(c_132892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126796,c_642]) ).

tcf(c_132893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126834,c_642]) ).

tcf(c_132894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126837,c_642]) ).

tcf(c_132895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126839,c_642]) ).

tcf(c_132896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127183,c_642]) ).

tcf(c_132897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127225,c_642]) ).

tcf(c_132898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128047,c_642]) ).

tcf(c_132899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128082,c_642]) ).

tcf(c_132900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129469,c_642]) ).

tcf(c_132901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129474,c_642]) ).

tcf(c_132902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129480,c_642]) ).

tcf(c_132903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129487,c_642]) ).

tcf(c_132904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129493,c_642]) ).

tcf(c_132905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129942,c_642]) ).

tcf(c_132906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_129951,c_642]) ).

tcf(c_132907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X6,X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X6,X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126585,c_642]) ).

tcf(c_132908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(c_Pair(X0,X6,X2,X3),X7,X8,X9)),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(c_Pair(X0,X6,X2,X3),X7,X8,X9)),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_97184,c_642]) ).

tcf(c_132909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X8),X6,X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X8),X6,X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_97186,c_642]) ).

tcf(c_132910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X8),X6,X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X8),X6,X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_97187,c_642]) ).

tcf(c_132911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_97192,c_642]) ).

tcf(c_132912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ~ c_Relation_Osingle__valued(X2,iPr_def_11,iPr_def_12)
      | ~ c_in(c_Pair(X0,X3,iPr_def_11,iPr_def_12),X2,iPr_def_13)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,tc_prod(iPr_def_11,iPr_def_12)) ),
    inference(superposition,[status(thm)],[c_7266,c_642]) ).

tcf(c_132922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ~ c_Relation_Osingle__valued(X2,iPr_def_11,iPr_def_12)
      | ~ c_in(c_Pair(X0,X3,iPr_def_11,iPr_def_12),X2,iPr_def_13)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,iPr_def_13) ),
    inference(light_normalisation,[status(thm)],[c_132912,c_7266]) ).

tcf(c_132927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ~ c_in(X0,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132806,c_755]) ).

tcf(c_132939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X4 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132871,c_125711]) ).

tcf(c_132957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132875,c_126533]) ).

tcf(c_132960,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132874,c_126528]) ).

tcf(c_132963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132873,c_125746]) ).

tcf(c_132966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132872,c_126082]) ).

tcf(c_132988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132877,c_126558]) ).

tcf(c_133004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132897,c_127225]) ).

tcf(c_133007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132896,c_127183]) ).

tcf(c_133010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132889,c_126871]) ).

tcf(c_133013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132888,c_126672]) ).

tcf(c_133016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132886,c_126665]) ).

tcf(c_133019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132885,c_126659]) ).

tcf(c_133022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132884,c_126584]) ).

tcf(c_133025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132882,c_126578]) ).

tcf(c_133028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132881,c_125942]) ).

tcf(c_133031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132880,c_126246]) ).

tcf(c_133034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132879,c_126286]) ).

tcf(c_133037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132878,c_126256]) ).

tcf(c_133046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132906,c_129951]) ).

tcf(c_133049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132905,c_129942]) ).

tcf(c_133052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132904,c_129493]) ).

tcf(c_133055,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132903,c_129487]) ).

tcf(c_133058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132902,c_129480]) ).

tcf(c_133061,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132901,c_129474]) ).

tcf(c_133064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132899,c_128082]) ).

tcf(c_133067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132898,c_128047]) ).

tcf(c_133098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_132911,c_97192]) ).

tcf(c_133441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3))) ),
    inference(superposition,[status(thm)],[c_563,c_784]) ).

tcf(c_133442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3))) ),
    inference(superposition,[status(thm)],[c_566,c_784]) ).

tcf(c_133443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,X0,X1,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_784]) ).

tcf(c_133444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,X0,X1,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_784]) ).

tcf(c_133445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X1))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,X1,X2,t_a)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_784]) ).

tcf(c_133446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X0,c_Relation_Oconverse(X3,X2,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_784]) ).

tcf(c_133447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_784]) ).

tcf(c_133449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X3))) ),
    inference(superposition,[status(thm)],[c_126015,c_784]) ).

tcf(c_133450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X4))) ),
    inference(superposition,[status(thm)],[c_126019,c_784]) ).

tcf(c_133451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X5))) ),
    inference(superposition,[status(thm)],[c_126024,c_784]) ).

tcf(c_133452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3))) ),
    inference(superposition,[status(thm)],[c_126026,c_784]) ).

tcf(c_133453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3))) ),
    inference(superposition,[status(thm)],[c_126028,c_784]) ).

tcf(c_133454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4))) ),
    inference(superposition,[status(thm)],[c_126079,c_784]) ).

tcf(c_133455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4))) ),
    inference(superposition,[status(thm)],[c_126084,c_784]) ).

tcf(c_133457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5))) ),
    inference(superposition,[status(thm)],[c_126110,c_784]) ).

tcf(c_133458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126112,c_784]) ).

tcf(c_133459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5))) ),
    inference(superposition,[status(thm)],[c_126143,c_784]) ).

tcf(c_133460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126242,c_784]) ).

tcf(c_133461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126149,c_784]) ).

tcf(c_133462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126155,c_784]) ).

tcf(c_133463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126161,c_784]) ).

tcf(c_133465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126249,c_784]) ).

tcf(c_133466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126289,c_784]) ).

tcf(c_133467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126295,c_784]) ).

tcf(c_133468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126397,c_784]) ).

tcf(c_133469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126399,c_784]) ).

tcf(c_133471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126413,c_784]) ).

tcf(c_133472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126717,c_784]) ).

tcf(c_133473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126724,c_784]) ).

tcf(c_133474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126759,c_784]) ).

tcf(c_133475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126766,c_784]) ).

tcf(c_133476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126774,c_784]) ).

tcf(c_133477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4))) ),
    inference(superposition,[status(thm)],[c_126082,c_784]) ).

tcf(c_133478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126781,c_784]) ).

tcf(c_133479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_126256,c_784]) ).

tcf(c_133480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_126246,c_784]) ).

tcf(c_133481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_126578,c_784]) ).

tcf(c_133482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_126659,c_784]) ).

tcf(c_133483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126789,c_784]) ).

tcf(c_133484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126796,c_784]) ).

tcf(c_133485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126837,c_784]) ).

tcf(c_133486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6))) ),
    inference(superposition,[status(thm)],[c_128047,c_784]) ).

tcf(c_133487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,c_Transitive__Closure_Otrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_784]) ).

tcf(c_133488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_784]) ).

tcf(c_133767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2)))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2))) ),
    inference(superposition,[status(thm)],[c_563,c_794]) ).

tcf(c_133768,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2)))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2))) ),
    inference(superposition,[status(thm)],[c_566,c_794]) ).

tcf(c_133769,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3)))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X2,X3))) ),
    inference(superposition,[status(thm)],[c_567,c_794]) ).

tcf(c_133770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3)))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X2,X3))) ),
    inference(superposition,[status(thm)],[c_568,c_794]) ).

tcf(c_133771,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X2,t_a)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_794]) ).

tcf(c_133772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X1,c_Relation_Oconverse(X3,X2,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_794]) ).

tcf(c_133773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_794]) ).

tcf(c_133775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3))) ),
    inference(superposition,[status(thm)],[c_126015,c_794]) ).

tcf(c_133776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X4))) ),
    inference(superposition,[status(thm)],[c_126019,c_794]) ).

tcf(c_133777,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X5))) ),
    inference(superposition,[status(thm)],[c_126024,c_794]) ).

tcf(c_133778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3))) ),
    inference(superposition,[status(thm)],[c_126026,c_794]) ).

tcf(c_133779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3))) ),
    inference(superposition,[status(thm)],[c_126028,c_794]) ).

tcf(c_133780,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4))) ),
    inference(superposition,[status(thm)],[c_126079,c_794]) ).

tcf(c_133781,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4))) ),
    inference(superposition,[status(thm)],[c_126084,c_794]) ).

tcf(c_133783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5))) ),
    inference(superposition,[status(thm)],[c_126110,c_794]) ).

tcf(c_133784,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126112,c_794]) ).

tcf(c_133785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5))) ),
    inference(superposition,[status(thm)],[c_126143,c_794]) ).

tcf(c_133786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126242,c_794]) ).

tcf(c_133787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126149,c_794]) ).

tcf(c_133788,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126155,c_794]) ).

tcf(c_133789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3))) ),
    inference(superposition,[status(thm)],[c_126161,c_794]) ).

tcf(c_133791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126249,c_794]) ).

tcf(c_133792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126289,c_794]) ).

tcf(c_133793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4))) ),
    inference(superposition,[status(thm)],[c_126295,c_794]) ).

tcf(c_133794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126397,c_794]) ).

tcf(c_133795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126399,c_794]) ).

tcf(c_133797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126413,c_794]) ).

tcf(c_133798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126717,c_794]) ).

tcf(c_133799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126724,c_794]) ).

tcf(c_133800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5))) ),
    inference(superposition,[status(thm)],[c_126759,c_794]) ).

tcf(c_133801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126766,c_794]) ).

tcf(c_133802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126774,c_794]) ).

tcf(c_133803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4))) ),
    inference(superposition,[status(thm)],[c_126082,c_794]) ).

tcf(c_133804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126781,c_794]) ).

tcf(c_133805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_126256,c_794]) ).

tcf(c_133806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_126246,c_794]) ).

tcf(c_133807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_126578,c_794]) ).

tcf(c_133808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_126659,c_794]) ).

tcf(c_133809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126789,c_794]) ).

tcf(c_133810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126796,c_794]) ).

tcf(c_133811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3))) ),
    inference(superposition,[status(thm)],[c_126837,c_794]) ).

tcf(c_133812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6))) ),
    inference(superposition,[status(thm)],[c_128047,c_794]) ).

tcf(c_133813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,c_Transitive__Closure_Otrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_794]) ).

tcf(c_133814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_794]) ).

tcf(c_134095,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_126708,c_841]) ).

tcf(c_134102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_126876,c_841]) ).

tcf(c_134109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_126877,c_841]) ).

tcf(c_134143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_127188,c_841]) ).

tcf(c_134150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_127189,c_841]) ).

tcf(c_134166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_127231,c_841]) ).

tcf(c_134168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_125590,c_841]) ).

tcf(c_134175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X3,tc_prod(X2,X2)),c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),tc_prod(X2,X2))
      | hBOOL(hAPP(X4,c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X0,X1,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_550]) ).

tcf(c_134176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X3,X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_125973]) ).

tcf(c_134177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X3,X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_125887]) ).

tcf(c_134178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_794]) ).

tcf(c_134179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_784]) ).

tcf(c_134180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_800]) ).

tcf(c_134181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2)))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_786]) ).

tcf(c_134182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_789]) ).

tcf(c_134183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_809]) ).

tcf(c_134184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_806]) ).

tcf(c_134185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_776]) ).

tcf(c_134186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_762]) ).

tcf(c_134187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_761]) ).

tcf(c_134188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_796]) ).

tcf(c_134189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X3,X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_772]) ).

tcf(c_134190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Relation_OId__on(X3,X2),X0,X1,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_635]) ).

tcf(c_134191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Relation_Oconverse(X3,X2,X2),X0,X1,X2),X0,X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_639]) ).

tcf(c_134192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2) = X4 )
      | ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_642]) ).

tcf(c_134193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Relation_OImage(X3,X4,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(X0,X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_774]) ).

tcf(c_134194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Relation_ODomain(c_Relation_Oconverse(X3,X2,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_770]) ).

tcf(c_134196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X4,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X3,X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_763]) ).

tcf(c_134197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_840]) ).

tcf(c_134198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Product__Type_OSigma(X3,X4,X2,X2),X0,X1,X2),hAPP(X4,X0),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X3,X4,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_766]) ).

tcf(c_134199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X3,X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X3,X4,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_765]) ).

tcf(c_134200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X0,X1,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_791]) ).

tcf(c_134347,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X3,tc_prod(X2,X2)),c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),tc_prod(X2,X2))
      | hBOOL(hAPP(X4,c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_550]) ).

tcf(c_134348,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),X2,t_a),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_803,c_560]) ).

tcf(c_134349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),X2,t_a)))
      | ( v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_803,c_564]) ).

tcf(c_134350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),X2,t_a),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_803,c_562]) ).

tcf(c_134351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),X2,t_a)))
      | ( v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_803,c_561]) ).

tcf(c_134352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,X3),X2,X3)))
      | ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,X3) = X0 )
      | ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_803,c_565]) ).

tcf(c_134353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X3,X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_125973]) ).

tcf(c_134354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X3,X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_125887]) ).

tcf(c_134355,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_794]) ).

tcf(c_134356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_784]) ).

tcf(c_134357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2)))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_800]) ).

tcf(c_134358,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_786]) ).

tcf(c_134359,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2) = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_789]) ).

tcf(c_134360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),c_Wellfounded_Oacc(X3,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_809]) ).

tcf(c_134361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2) = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_806]) ).

tcf(c_134362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),c_Wellfounded_Oacc(X3,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_776]) ).

tcf(c_134363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_762]) ).

tcf(c_134364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_761]) ).

tcf(c_134365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_796]) ).

tcf(c_134366,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Relation_OId__on(X3,X2),X2),X3,X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_772]) ).

tcf(c_134367,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Relation_OId__on(X3,X2),X2) = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_635]) ).

tcf(c_134368,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Relation_Oconverse(X3,X2,X2),X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_639]) ).

tcf(c_134369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X1 = X4 )
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X2,X3,X3)
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_803,c_642]) ).

tcf(c_134370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Relation_OImage(X3,X4,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_774]) ).

tcf(c_134372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_768]) ).

tcf(c_134373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X4,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X3,X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_763]) ).

tcf(c_134374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_840]) ).

tcf(c_134375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Product__Type_OSigma(X3,X4,X2,X2),X2)),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X3,X4,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_766]) ).

tcf(c_134376,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Product__Type_OSigma(X3,X4,X2,X2),X2),X3,X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X3,X4,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_765]) ).

tcf(c_134377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_791]) ).

tcf(c_134545,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Otrancl(X2,t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_626,c_792]) ).

tcf(c_134546,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_853,c_792]) ).

tcf(c_134547,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_125973]) ).

tcf(c_134548,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_125887]) ).

tcf(c_134549,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X0))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X3,X0,X2,t_a)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_794]) ).

tcf(c_134550,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X2,t_a)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_784]) ).

tcf(c_134551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X2,t_a)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_800]) ).

tcf(c_134552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,X0,X2,t_a)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_786]) ).

tcf(c_134553,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_789]) ).

tcf(c_134554,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X2,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),c_Wellfounded_Oacc(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_809]) ).

tcf(c_134555,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(X2,t_a,t_a),t_a)
      | ( X0 = X1 )
      | ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_806]) ).

tcf(c_134556,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_776]) ).

tcf(c_134557,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X3,c_Transitive__Closure_Ortrancl(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_762]) ).

tcf(c_134558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X3,t_a)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X3,c_Transitive__Closure_Ortrancl(X2,t_a),t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_761]) ).

tcf(c_134559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = X1 )
      | ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2) = X3 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a)
      | ~ c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_642]) ).

tcf(c_134560,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,t_a),X3,t_a,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(X0,X3,t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_774]) ).

tcf(c_134561,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a),t_a,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_770]) ).

tcf(c_134562,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a),t_a)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_768]) ).

tcf(c_134563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),X3,tc_prod(tc_prod(t_a,t_a),tc_prod(t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(X2,t_a),X3,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_763]) ).

tcf(c_134564,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X2,t_a),c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_840]) ).

tcf(c_134565,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Relation_Oconverse(X2,t_a,t_a)),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,t_a,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_791]) ).

tcf(c_134704,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_783]) ).

tcf(c_134705,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_783]) ).

tcf(c_134706,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_125973]) ).

tcf(c_134707,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_125887]) ).

tcf(c_134708,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_794]) ).

tcf(c_134709,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_784]) ).

tcf(c_134710,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_800]) ).

tcf(c_134711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_786]) ).

tcf(c_134712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_789]) ).

tcf(c_134713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_809]) ).

tcf(c_134714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2) = X0 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_806]) ).

tcf(c_134715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_776]) ).

tcf(c_134716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_762]) ).

tcf(c_134717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_761]) ).

tcf(c_134718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2) = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_642]) ).

tcf(c_134719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X4,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(X0,X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_774]) ).

tcf(c_134720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_770]) ).

tcf(c_134722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X4,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(X3,X2),X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_763]) ).

tcf(c_134723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X3,X2),c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_840]) ).

tcf(c_134724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Relation_Oconverse(X3,X2,X2),X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_791]) ).

tcf(c_134850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_127232,c_841]) ).

tcf(c_134861,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_705,c_127263]) ).

tcf(c_134862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X2)
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_731,c_127263]) ).

tcf(c_134873,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(X2,X1,t_a)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a)))) ),
    inference(superposition,[status(thm)],[c_134861,c_553]) ).

tcf(c_134875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,X1,X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_OId__on(X1,X2),X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_134861,c_550]) ).

tcf(c_134876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134861,c_560]) ).

tcf(c_134877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134861,c_564]) ).

tcf(c_134878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134861,c_562]) ).

tcf(c_134879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134861,c_561]) ).

tcf(c_134880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_134861,c_565]) ).

tcf(c_134881,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,X0,tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_134861,c_125973]) ).

tcf(c_134882,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,X0,tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_134861,c_125887]) ).

tcf(c_134883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X0,X2,X2),X1,tc_prod(X2,X2))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_134861,c_776]) ).

tcf(c_134884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_134861,c_762]) ).

tcf(c_134885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_134861,c_761]) ).

tcf(c_134886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X3),X4,tc_prod(X2,X3))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X3)),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134861,c_642]) ).

tcf(c_134887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X5),X4,tc_prod(X2,X5))
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X5)),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134861,c_774]) ).

tcf(c_134888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X2,X3),X1,tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_134861,c_770]) ).

tcf(c_134889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_134861,c_768]) ).

tcf(c_134890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X1)
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_134861,c_763]) ).

tcf(c_134891,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,X0,X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_134861,c_840]) ).

tcf(c_134990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134891,c_517]) ).

tcf(c_134991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_134891,c_537]) ).

tcf(c_134992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_134891,c_841]) ).

tcf(c_135009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134992,c_560]) ).

tcf(c_135010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134992,c_564]) ).

tcf(c_135011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134992,c_562]) ).

tcf(c_135012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134992,c_561]) ).

tcf(c_135013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3,X3),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_134992,c_565]) ).

tcf(c_135014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_134992,c_125973]) ).

tcf(c_135015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_134992,c_125887]) ).

tcf(c_135016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X3,X3),X1,X2)
      | c_in(X4,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_134992,c_776]) ).

tcf(c_135017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_134992,c_762]) ).

tcf(c_135018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_134992,c_761]) ).

tcf(c_135019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X3),X4,X5)
      | ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134992,c_642]) ).

tcf(c_135020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X6),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134992,c_774]) ).

tcf(c_135021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X3,X4),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_134992,c_770]) ).

tcf(c_135022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X3,X4),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3,X4),X3) ),
    inference(superposition,[status(thm)],[c_134992,c_768]) ).

tcf(c_135023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X1)
      | c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_134992,c_763]) ).

tcf(c_135101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135014,c_517]) ).

tcf(c_135102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_135014,c_537]) ).

tcf(c_135103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_135014,c_841]) ).

tcf(c_135116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135015,c_517]) ).

tcf(c_135117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_135015,c_537]) ).

tcf(c_135118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_135015,c_841]) ).

tcf(c_135148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135103,c_560]) ).

tcf(c_135149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135103,c_564]) ).

tcf(c_135150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135103,c_562]) ).

tcf(c_135151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135103,c_561]) ).

tcf(c_135152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4,X4),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_135103,c_565]) ).

tcf(c_135153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_135103,c_125973]) ).

tcf(c_135154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_135103,c_125887]) ).

tcf(c_135155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X1,X5,X4,X4),X2,X3)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4))) ),
    inference(superposition,[status(thm)],[c_135103,c_794]) ).

tcf(c_135156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X5,X1,X4,X4),X2,X3)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4))) ),
    inference(superposition,[status(thm)],[c_135103,c_784]) ).

tcf(c_135157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X5,X1,X4,X4),X2,X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_135103,c_800]) ).

tcf(c_135158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X1,X5,X4,X4),X2,X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_135103,c_786]) ).

tcf(c_135159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_135103,c_789]) ).

tcf(c_135161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X4,X4),X2,X3)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_135103,c_806]) ).

tcf(c_135162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X4,X4),X1,X2)
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_135103,c_776]) ).

tcf(c_135163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | c_in(c_Pair(X5,X6,X4,X4),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_135103,c_762]) ).

tcf(c_135164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,X0,X4)
      | c_in(c_Pair(X5,X6,X4,X4),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_135103,c_761]) ).

tcf(c_135165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X3),X4,X5)
      | ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_135103,c_642]) ).

tcf(c_135166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X7),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_135103,c_774]) ).

tcf(c_135167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X4,X5),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X5,X4),X5) ),
    inference(superposition,[status(thm)],[c_135103,c_770]) ).

tcf(c_135168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X4,X5),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X4) ),
    inference(superposition,[status(thm)],[c_135103,c_768]) ).

tcf(c_135169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_135103,c_763]) ).

tcf(c_135291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135118,c_560]) ).

tcf(c_135292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135118,c_564]) ).

tcf(c_135293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135118,c_562]) ).

tcf(c_135294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135118,c_561]) ).

tcf(c_135295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4,X4),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_135118,c_565]) ).

tcf(c_135296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_135118,c_125973]) ).

tcf(c_135297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_135118,c_125887]) ).

tcf(c_135298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X4,X4),X1,X2)
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_135118,c_776]) ).

tcf(c_135299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | c_in(c_Pair(X5,X6,X4,X4),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_135118,c_762]) ).

tcf(c_135300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,X0,X4)
      | c_in(c_Pair(X5,X6,X4,X4),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_135118,c_761]) ).

tcf(c_135301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135118,c_796]) ).

tcf(c_135302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X3),X4,X5)
      | ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_135118,c_642]) ).

tcf(c_135303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X7),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_135118,c_774]) ).

tcf(c_135304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X4,X5),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X5,X4),X5) ),
    inference(superposition,[status(thm)],[c_135118,c_770]) ).

tcf(c_135305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X4,X5),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X4) ),
    inference(superposition,[status(thm)],[c_135118,c_768]) ).

tcf(c_135306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_135118,c_763]) ).

tcf(c_135387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(t_a,t_a)),tc_prod(t_a,t_a),X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(t_a,t_a)),tc_prod(t_a,t_a),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127840,c_562]) ).

tcf(c_135388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(t_a,t_a)),tc_prod(t_a,t_a),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127840,c_561]) ).

tcf(c_135389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(X4,X4)),tc_prod(X4,X4),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_127840,c_565]) ).

tcf(c_135390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,tc_prod(X3,X3)),tc_prod(X3,X3),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_127840,c_125973]) ).

tcf(c_135391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,tc_prod(X3,X3)),tc_prod(X3,X3),X2),X3),X4)),
    inference(superposition,[status(thm)],[c_127840,c_125887]) ).

tcf(c_135392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(X4,X4)),tc_prod(X4,X4),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(X4,X4)),tc_prod(X4,X4),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_127840,c_776]) ).

tcf(c_135393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(X4,X4)),tc_prod(X4,X4),X3),X4) ),
    inference(superposition,[status(thm)],[c_127840,c_762]) ).

tcf(c_135395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,tc_prod(X2,X3)),tc_prod(X2,X3),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,tc_prod(X2,X3)),tc_prod(X2,X3),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127840,c_642]) ).

tcf(c_135396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,tc_prod(X2,X7)),tc_prod(X2,X7),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127840,c_774]) ).

tcf(c_135397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(X4,X5)),tc_prod(X4,X5),X3),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_127840,c_770]) ).

tcf(c_135398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,tc_prod(X4,X5)),tc_prod(X4,X5),X3),X4,X5),X4),
    inference(superposition,[status(thm)],[c_127840,c_768]) ).

tcf(c_135399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X3,X3),X4,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X3,X2),X4,X3) ),
    inference(superposition,[status(thm)],[c_127840,c_763]) ).

tcf(c_135400,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X3,X2),X4)),
    inference(superposition,[status(thm)],[c_127840,c_840]) ).

tcf(c_135418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,tc_prod(X3,X4)),tc_prod(X3,X4),X2),X3,X4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_135395,c_127840]) ).

tcf(c_135456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_128590,c_560]) ).

tcf(c_135457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_128590,c_564]) ).

tcf(c_135458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_128590,c_562]) ).

tcf(c_135459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(t_a,t_a)),X3,tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_128590,c_561]) ).

tcf(c_135460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X5))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(X3,X3)),X4,tc_prod(X3,X3),tc_prod(X3,X3)),X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,tc_prod(X3,X3)),X4,tc_prod(X3,X3),tc_prod(X3,X3)),X3),X3,X3),X4,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_128590,c_565]) ).

tcf(c_135461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X1,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128590,c_125973]) ).

tcf(c_135462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X1,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128590,c_125887]) ).

tcf(c_135463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_128590,c_776]) ).

tcf(c_135464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_in(c_Pair(X4,X5,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3,tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_128590,c_762]) ).

tcf(c_135465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X2)
      | ~ c_in(c_Pair(X4,X5,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3,tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_128590,c_761]) ).

tcf(c_135466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X6 )
      | ~ c_in(c_Pair(X0,X6,X2,X3),X5,tc_prod(X2,X3))
      | ~ c_Relation_Osingle__valued(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5,tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128590,c_642]) ).

tcf(c_135467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Relation_OImage(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X6,tc_prod(X2,X3)),X4,tc_prod(X2,X3),tc_prod(X2,X3)),X5,X2,X3),X3)
      | ~ c_in(X0,X5,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128590,c_774]) ).

tcf(c_135468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X5,tc_prod(X2,X3)),X4,tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128590,c_770]) ).

tcf(c_135469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X5,tc_prod(X2,X3)),X4,tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128590,c_768]) ).

tcf(c_135470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X4,X1,X1),X3,tc_prod(X1,X1))
      | ~ c_in(X4,X2,X1)
      | ~ c_Relation_Orefl__on(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1,X1),X3,X1) ),
    inference(superposition,[status(thm)],[c_128590,c_763]) ).

tcf(c_135471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X1,X2,X2),X0))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_128590,c_840]) ).

tcf(c_135637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X2,X2),X3),X0)),
    inference(superposition,[status(thm)],[c_743,c_125591]) ).

tcf(c_135638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X6),
    inference(superposition,[status(thm)],[c_125591,c_841]) ).

tcf(c_135645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_802]) ).

tcf(c_135646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_802]) ).

tcf(c_135647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ( v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_802,c_560]) ).

tcf(c_135648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a)))
      | ( v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_802,c_564]) ).

tcf(c_135649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ( v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_802,c_562]) ).

tcf(c_135650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a)))
      | ( v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)) = X0 )
      | ~ c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Ortrancl(X2,t_a)),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_802,c_561]) ).

tcf(c_135651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)))
      | ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3) = X0 )
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3),X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_802,c_565]) ).

tcf(c_135652,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_125973]) ).

tcf(c_135653,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_125887]) ).

tcf(c_135654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_794]) ).

tcf(c_135655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_784]) ).

tcf(c_135656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_800]) ).

tcf(c_135657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X3,X2)))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_786]) ).

tcf(c_135658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2) = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_789]) ).

tcf(c_135659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Wellfounded_Oacc(X3,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(X1,c_Wellfounded_Oacc(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_809]) ).

tcf(c_135660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Relation_ODomain(X3,X2,X2),X2)
      | ( X0 = X1 )
      | ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2) = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_806]) ).

tcf(c_135661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ( X0 = X1 )
      | ~ c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_776]) ).

tcf(c_135662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_762]) ).

tcf(c_135663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2)
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(X4,c_Transitive__Closure_Ortrancl(X3,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_761]) ).

tcf(c_135664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X2 = X4 )
      | ( X1 = X2 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(X0,X3),X3,X3)
      | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_802,c_642]) ).

tcf(c_135665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X4,X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_774]) ).

tcf(c_135666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_770]) ).

tcf(c_135667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_768]) ).

tcf(c_135668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2),tc_prod(X2,X2),tc_prod(X2,X2)),X4,tc_prod(tc_prod(X2,X2),tc_prod(X2,X2)))
      | ( X0 = X1 )
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(X3,X2),X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_763]) ).

tcf(c_135669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X3,X2),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2)))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_840]) ).

tcf(c_135670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Relation_Oconverse(X3,X2,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_791]) ).

tcf(c_135797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X3,X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_633]) ).

tcf(c_135798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X3,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X3,X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_633]) ).

tcf(c_135799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X3,X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X3,X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_633]) ).

tcf(c_135800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X3,X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X3,X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_633]) ).

tcf(c_135801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_633]) ).

tcf(c_135802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_633]) ).

tcf(c_135803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_OId__on(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(X0,X3,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_771,c_633]) ).

tcf(c_135804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Product__Type_OSigma(X3,X4,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(X5,X3,X2)
      | ~ c_in(X0,hAPP(X4,X5),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Product__Type_OSigma(X3,X4,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_778,c_633]) ).

tcf(c_135805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X3),tc_prod(X3,X3))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_783,c_633]) ).

tcf(c_135806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_633]) ).

tcf(c_135807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_633]) ).

tcf(c_135808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_633]) ).

tcf(c_135809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Otrancl(X0,X3),tc_prod(X3,X3))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),X0,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_801,c_633]) ).

tcf(c_135810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_633]) ).

tcf(c_135811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_633]) ).

tcf(c_135812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_633]) ).

tcf(c_135813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125697,c_633]) ).

tcf(c_135814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125698,c_633]) ).

tcf(c_135815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125699,c_633]) ).

tcf(c_135816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125781,c_633]) ).

tcf(c_135817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125928,c_633]) ).

tcf(c_135818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125931,c_633]) ).

tcf(c_135819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125935,c_633]) ).

tcf(c_135820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125797,c_633]) ).

tcf(c_135821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125747,c_633]) ).

tcf(c_135822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125794,c_633]) ).

tcf(c_135823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125796,c_633]) ).

tcf(c_135824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125799,c_633]) ).

tcf(c_135825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125939,c_633]) ).

tcf(c_135826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125952,c_633]) ).

tcf(c_135827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126382,c_633]) ).

tcf(c_135828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126383,c_633]) ).

tcf(c_135829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126015,c_633]) ).

tcf(c_135830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126019,c_633]) ).

tcf(c_135831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126024,c_633]) ).

tcf(c_135832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126026,c_633]) ).

tcf(c_135833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126028,c_633]) ).

tcf(c_135834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126030,c_633]) ).

tcf(c_135835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126079,c_633]) ).

tcf(c_135836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126084,c_633]) ).

tcf(c_135837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126086,c_633]) ).

tcf(c_135838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126107,c_633]) ).

tcf(c_135839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126110,c_633]) ).

tcf(c_135840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126112,c_633]) ).

tcf(c_135841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126143,c_633]) ).

tcf(c_135842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126146,c_633]) ).

tcf(c_135843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126242,c_633]) ).

tcf(c_135844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126149,c_633]) ).

tcf(c_135845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126152,c_633]) ).

tcf(c_135846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126155,c_633]) ).

tcf(c_135847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126158,c_633]) ).

tcf(c_135848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126161,c_633]) ).

tcf(c_135849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126163,c_633]) ).

tcf(c_135850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126394,c_633]) ).

tcf(c_135851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126249,c_633]) ).

tcf(c_135852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126252,c_633]) ).

tcf(c_135853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126289,c_633]) ).

tcf(c_135854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126292,c_633]) ).

tcf(c_135855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126295,c_633]) ).

tcf(c_135856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126297,c_633]) ).

tcf(c_135857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126397,c_633]) ).

tcf(c_135858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126399,c_633]) ).

tcf(c_135859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126404,c_633]) ).

tcf(c_135860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126409,c_633]) ).

tcf(c_135861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126413,c_633]) ).

tcf(c_135862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126714,c_633]) ).

tcf(c_135863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126717,c_633]) ).

tcf(c_135864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126720,c_633]) ).

tcf(c_135865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126724,c_633]) ).

tcf(c_135866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126755,c_633]) ).

tcf(c_135867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126759,c_633]) ).

tcf(c_135868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126762,c_633]) ).

tcf(c_135869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126766,c_633]) ).

tcf(c_135870,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126770,c_633]) ).

tcf(c_135871,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126774,c_633]) ).

tcf(c_135872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126777,c_633]) ).

tcf(c_135873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125711,c_633]) ).

tcf(c_135874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126082,c_633]) ).

tcf(c_135875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125746,c_633]) ).

tcf(c_135876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126528,c_633]) ).

tcf(c_135877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126533,c_633]) ).

tcf(c_135878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126781,c_633]) ).

tcf(c_135879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126558,c_633]) ).

tcf(c_135880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126256,c_633]) ).

tcf(c_135881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126286,c_633]) ).

tcf(c_135882,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126246,c_633]) ).

tcf(c_135883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125942,c_633]) ).

tcf(c_135884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126578,c_633]) ).

tcf(c_135885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126785,c_633]) ).

tcf(c_135886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126584,c_633]) ).

tcf(c_135887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126659,c_633]) ).

tcf(c_135888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126665,c_633]) ).

tcf(c_135889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125830,c_633]) ).

tcf(c_135890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126672,c_633]) ).

tcf(c_135891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126871,c_633]) ).

tcf(c_135892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126789,c_633]) ).

tcf(c_135893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126792,c_633]) ).

tcf(c_135894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126796,c_633]) ).

tcf(c_135895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126834,c_633]) ).

tcf(c_135896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126837,c_633]) ).

tcf(c_135897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126839,c_633]) ).

tcf(c_135898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127183,c_633]) ).

tcf(c_135899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127225,c_633]) ).

tcf(c_135900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,tc_prod(X2,X2)),tc_prod(X2,X2),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,tc_prod(X2,X2)),tc_prod(X2,X2),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127840,c_633]) ).

tcf(c_135901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128047,c_633]) ).

tcf(c_135902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128082,c_633]) ).

tcf(c_135903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4,tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X5,X0,X2,X2),X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128590,c_633]) ).

tcf(c_135904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129469,c_633]) ).

tcf(c_135905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129474,c_633]) ).

tcf(c_135906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129480,c_633]) ).

tcf(c_135907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129487,c_633]) ).

tcf(c_135908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129493,c_633]) ).

tcf(c_135909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129942,c_633]) ).

tcf(c_135910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_129951,c_633]) ).

tcf(c_135911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126585,c_633]) ).

tcf(c_135912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134992,c_633]) ).

tcf(c_135913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135103,c_633]) ).

tcf(c_135914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135118,c_633]) ).

tcf(c_135915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(c_Pair(X5,X0,X2,X2),X6,X7,X8)),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(c_Pair(X5,X0,X2,X2),X6,X7,X8)),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_97184,c_633]) ).

tcf(c_135916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X7),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X7),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_97186,c_633]) ).

tcf(c_135917,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X7),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X7),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_97187,c_633]) ).

tcf(c_135918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_97192,c_633]) ).

tcf(c_135992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135910,c_129951]) ).

tcf(c_135993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135909,c_129942]) ).

tcf(c_135994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135908,c_129493]) ).

tcf(c_135995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135907,c_129487]) ).

tcf(c_135996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135906,c_129480]) ).

tcf(c_135997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135905,c_129474]) ).

tcf(c_135998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135902,c_128082]) ).

tcf(c_135999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135901,c_128047]) ).

tcf(c_136028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135918,c_97192]) ).

tcf(c_136152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,tc_prod(X2,X2)),tc_prod(X2,X2),X5),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_135900,c_127840]) ).

tcf(c_136394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X1,X2),X2),X2)
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X1,X2),X3,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_637]) ).

tcf(c_136395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X1,X2),X2),X2)
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X1,X2),X3,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_637]) ).

tcf(c_136396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,c_Transitive__Closure_Otrancl(X2,X3),X3,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_567,c_637]) ).

tcf(c_136397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,c_Transitive__Closure_Otrancl(X2,X3),X3,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_568,c_637]) ).

tcf(c_136398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_637]) ).

tcf(c_136399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,t_a),t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,c_Transitive__Closure_Otrancl(X3,t_a)),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_637]) ).

tcf(c_136400,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_637]) ).

tcf(c_136401,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X2,X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),tc_prod(X4,X4))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,c_Transitive__Closure_Otrancl(X3,X4),X4),X4,X4),X3,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_803,c_637]) ).

tcf(c_136402,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125928,c_637]) ).

tcf(c_136403,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125931,c_637]) ).

tcf(c_136404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125935,c_637]) ).

tcf(c_136405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125797,c_637]) ).

tcf(c_136406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125747,c_637]) ).

tcf(c_136408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125796,c_637]) ).

tcf(c_136409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125799,c_637]) ).

tcf(c_136410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125939,c_637]) ).

tcf(c_136412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126382,c_637]) ).

tcf(c_136413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126383,c_637]) ).

tcf(c_136414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126030,c_637]) ).

tcf(c_136415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126086,c_637]) ).

tcf(c_136416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126146,c_637]) ).

tcf(c_136417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126152,c_637]) ).

tcf(c_136418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126158,c_637]) ).

tcf(c_136419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126163,c_637]) ).

tcf(c_136420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126252,c_637]) ).

tcf(c_136421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126292,c_637]) ).

tcf(c_136422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126297,c_637]) ).

tcf(c_136424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126714,c_637]) ).

tcf(c_136425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126720,c_637]) ).

tcf(c_136426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126755,c_637]) ).

tcf(c_136427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126762,c_637]) ).

tcf(c_136428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126770,c_637]) ).

tcf(c_136429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126777,c_637]) ).

tcf(c_136430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125746,c_637]) ).

tcf(c_136431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126286,c_637]) ).

tcf(c_136432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125942,c_637]) ).

tcf(c_136433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126785,c_637]) ).

tcf(c_136434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126584,c_637]) ).

tcf(c_136435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126665,c_637]) ).

tcf(c_136436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126792,c_637]) ).

tcf(c_136437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126834,c_637]) ).

tcf(c_136438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126839,c_637]) ).

tcf(c_136439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128082,c_637]) ).

tcf(c_136440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X3,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X3,X2,X2),X4,X5,X6)),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126585,c_637]) ).

tcf(c_136441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X5,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135118,c_637]) ).

tcf(c_136442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_637]) ).

tcf(c_136644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_638]) ).

tcf(c_136645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_638]) ).

tcf(c_136646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_638]) ).

tcf(c_136647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_638]) ).

tcf(c_136649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Otrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_638]) ).

tcf(c_136650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X3,X1),X4,X1,X1),X0,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_638]) ).

tcf(c_136651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_638]) ).

tcf(c_136692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_638]) ).

tcf(c_136716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X3,X1),X4,X1,X1),X0,tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_136650,c_626]) ).

tcf(c_136744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),X3)
      | ~ c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_130430]) ).

tcf(c_136745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),t_a),t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3)),t_a,t_a),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_560]) ).

tcf(c_136746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3)),t_a,t_a),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_564]) ).

tcf(c_136747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),t_a),t_a)
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3)),t_a,t_a),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_562]) ).

tcf(c_136748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3)),t_a,t_a),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_561]) ).

tcf(c_136749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X5))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),X4),X4)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),X4),X4,X4),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_565]) ).

tcf(c_136750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X3),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_125973]) ).

tcf(c_136751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X3),X0))
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_125887]) ).

tcf(c_136752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X5,X0,X2,X2),X3,tc_prod(X4,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_633]) ).

tcf(c_136753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),X2),X2)
      | ~ c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_130430,c_776]) ).

tcf(c_136754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,X5,X2)
      | ~ c_Relation_Orefl__on(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_130430,c_762]) ).

tcf(c_136755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,X5,X2)
      | ~ c_Relation_Orefl__on(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X4),X4),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_130430,c_761]) ).

tcf(c_136757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_637]) ).

tcf(c_136758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_796]) ).

tcf(c_136759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X4,X5),X5),X2,X3)
      | ~ c_in(c_Pair(X0,X6,X2,X3),X4,tc_prod(X5,X5))
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X4,X5),X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_642]) ).

tcf(c_136760,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X4,X5),X5),X6,X2,X3),X3)
      | ~ c_in(X0,X6,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X5,X5)) ),
    inference(superposition,[status(thm)],[c_130430,c_774]) ).

tcf(c_136761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X4,X5),X5),X2,X3),X3,X2),X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X5,X5)) ),
    inference(superposition,[status(thm)],[c_130430,c_770]) ).

tcf(c_136762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X4,X5),X5),X2,X3),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X5,X5)) ),
    inference(superposition,[status(thm)],[c_130430,c_768]) ).

tcf(c_136763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_in(X4,X0,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_130430,c_763]) ).

tcf(c_136838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130441,c_125973]) ).

tcf(c_136839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130441,c_125887]) ).

tcf(c_136840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130441,c_633]) ).

tcf(c_136841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130441,c_776]) ).

tcf(c_136842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130441,c_762]) ).

tcf(c_136843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130441,c_761]) ).

tcf(c_136845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130441,c_637]) ).

tcf(c_136846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130441,c_796]) ).

tcf(c_136847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130441,c_642]) ).

tcf(c_136848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130441,c_774]) ).

tcf(c_136849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130441,c_770]) ).

tcf(c_136850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130441,c_768]) ).

tcf(c_136851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130441,c_763]) ).

tcf(c_136961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130446,c_562]) ).

tcf(c_136962,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130446,c_561]) ).

tcf(c_136963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130446,c_565]) ).

tcf(c_136964,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130446,c_125973]) ).

tcf(c_136965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130446,c_125887]) ).

tcf(c_136966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130446,c_633]) ).

tcf(c_136967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130446,c_776]) ).

tcf(c_136968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130446,c_762]) ).

tcf(c_136972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130446,c_796]) ).

tcf(c_136973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130446,c_642]) ).

tcf(c_136974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130446,c_774]) ).

tcf(c_136975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130446,c_770]) ).

tcf(c_136976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130446,c_768]) ).

tcf(c_136977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130446,c_763]) ).

tcf(c_136996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_136973,c_130446]) ).

tcf(c_136999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_136966,c_130446]) ).

tcf(c_137027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130451,c_125973]) ).

tcf(c_137028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130451,c_125887]) ).

tcf(c_137029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130451,c_794]) ).

tcf(c_137030,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130451,c_784]) ).

tcf(c_137031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130451,c_800]) ).

tcf(c_137032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130451,c_786]) ).

tcf(c_137033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130451,c_789]) ).

tcf(c_137035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130451,c_806]) ).

tcf(c_137036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130451,c_633]) ).

tcf(c_137037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130451,c_776]) ).

tcf(c_137038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130451,c_762]) ).

tcf(c_137039,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130451,c_761]) ).

tcf(c_137040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130451,c_642]) ).

tcf(c_137041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130451,c_774]) ).

tcf(c_137042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130451,c_770]) ).

tcf(c_137043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130451,c_768]) ).

tcf(c_137044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130451,c_763]) ).

tcf(c_137101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130457,c_562]) ).

tcf(c_137102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130457,c_561]) ).

tcf(c_137103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130457,c_565]) ).

tcf(c_137104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130457,c_125973]) ).

tcf(c_137105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130457,c_125887]) ).

tcf(c_137106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130457,c_794]) ).

tcf(c_137107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130457,c_784]) ).

tcf(c_137108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130457,c_800]) ).

tcf(c_137109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130457,c_786]) ).

tcf(c_137112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130457,c_806]) ).

tcf(c_137113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130457,c_633]) ).

tcf(c_137114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130457,c_776]) ).

tcf(c_137115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130457,c_762]) ).

tcf(c_137117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130457,c_642]) ).

tcf(c_137118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130457,c_774]) ).

tcf(c_137119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130457,c_770]) ).

tcf(c_137120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130457,c_768]) ).

tcf(c_137121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130457,c_763]) ).

tcf(c_137154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_137117,c_130457]) ).

tcf(c_137157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_137113,c_130457]) ).

tcf(c_137208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_130912,c_125973]) ).

tcf(c_137209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),X0)),
    inference(superposition,[status(thm)],[c_130912,c_125887]) ).

tcf(c_137210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3))) ),
    inference(superposition,[status(thm)],[c_130912,c_794]) ).

tcf(c_137211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),X3))) ),
    inference(superposition,[status(thm)],[c_130912,c_784]) ).

tcf(c_137212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130912,c_800]) ).

tcf(c_137213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130912,c_786]) ).

tcf(c_137214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X2),X3,X4,X5)),X4,X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130912,c_789]) ).

tcf(c_137216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X2),X3,X4,X5)),X4,X5),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130912,c_806]) ).

tcf(c_137217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130912,c_633]) ).

tcf(c_137218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X4,X5),X6),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X2),X3,X4,X5)),X4,X5),X6),X2),X2) ),
    inference(superposition,[status(thm)],[c_130912,c_776]) ).

tcf(c_137219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_130912,c_762]) ).

tcf(c_137220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X7),X3) ),
    inference(superposition,[status(thm)],[c_130912,c_761]) ).

tcf(c_137221,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X6,X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X4,X2,X3),X5,X6,X7)),X6,X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130912,c_642]) ).

tcf(c_137222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X4),X5,X6,X7)),X6,X7),X8),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130912,c_774]) ).

tcf(c_137223,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X0,X2,X3),X4,X5,X6)),X5,X6),X7),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_130912,c_770]) ).

tcf(c_137224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,X2,X3),X4,X5,X6)),X5,X6),X7),X2,X3),X2),
    inference(superposition,[status(thm)],[c_130912,c_768]) ).

tcf(c_137225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X0,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130912,c_763]) ).

tcf(c_137278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130915,c_125973]) ).

tcf(c_137279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130915,c_125887]) ).

tcf(c_137280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130915,c_794]) ).

tcf(c_137281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130915,c_784]) ).

tcf(c_137282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130915,c_800]) ).

tcf(c_137283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130915,c_786]) ).

tcf(c_137284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130915,c_789]) ).

tcf(c_137286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130915,c_806]) ).

tcf(c_137287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130915,c_633]) ).

tcf(c_137288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130915,c_776]) ).

tcf(c_137289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130915,c_762]) ).

tcf(c_137290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130915,c_761]) ).

tcf(c_137291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130915,c_642]) ).

tcf(c_137292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130915,c_774]) ).

tcf(c_137293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130915,c_770]) ).

tcf(c_137294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130915,c_768]) ).

tcf(c_137295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130915,c_763]) ).

tcf(c_137399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130918,c_125973]) ).

tcf(c_137400,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130918,c_125887]) ).

tcf(c_137401,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130918,c_633]) ).

tcf(c_137402,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130918,c_776]) ).

tcf(c_137403,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130918,c_762]) ).

tcf(c_137404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130918,c_761]) ).

tcf(c_137406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130918,c_637]) ).

tcf(c_137407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130918,c_796]) ).

tcf(c_137408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130918,c_642]) ).

tcf(c_137409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130918,c_774]) ).

tcf(c_137410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130918,c_770]) ).

tcf(c_137411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130918,c_768]) ).

tcf(c_137412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130918,c_763]) ).

tcf(c_137468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130925,c_562]) ).

tcf(c_137469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130925,c_561]) ).

tcf(c_137470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130925,c_565]) ).

tcf(c_137471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130925,c_125973]) ).

tcf(c_137472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130925,c_125887]) ).

tcf(c_137473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130925,c_794]) ).

tcf(c_137474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130925,c_784]) ).

tcf(c_137475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130925,c_800]) ).

tcf(c_137476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130925,c_786]) ).

tcf(c_137479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130925,c_806]) ).

tcf(c_137480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130925,c_633]) ).

tcf(c_137481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130925,c_776]) ).

tcf(c_137482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130925,c_762]) ).

tcf(c_137484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130925,c_642]) ).

tcf(c_137485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130925,c_774]) ).

tcf(c_137486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130925,c_770]) ).

tcf(c_137487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130925,c_768]) ).

tcf(c_137488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130925,c_763]) ).

tcf(c_137521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_137484,c_130925]) ).

tcf(c_137524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_137480,c_130925]) ).

tcf(c_137552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130932,c_562]) ).

tcf(c_137553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130932,c_561]) ).

tcf(c_137554,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130932,c_565]) ).

tcf(c_137555,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130932,c_125973]) ).

tcf(c_137556,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130932,c_125887]) ).

tcf(c_137557,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130932,c_633]) ).

tcf(c_137558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130932,c_776]) ).

tcf(c_137559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130932,c_762]) ).

tcf(c_137563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130932,c_796]) ).

tcf(c_137564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130932,c_642]) ).

tcf(c_137565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130932,c_774]) ).

tcf(c_137566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130932,c_770]) ).

tcf(c_137567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130932,c_768]) ).

tcf(c_137568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130932,c_763]) ).

tcf(c_137587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_137564,c_130932]) ).

tcf(c_137590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_137557,c_130932]) ).

tcf(c_137716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130936,c_125973]) ).

tcf(c_137717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130936,c_125887]) ).

tcf(c_137718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130936,c_794]) ).

tcf(c_137719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130936,c_784]) ).

tcf(c_137720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130936,c_800]) ).

tcf(c_137721,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130936,c_786]) ).

tcf(c_137722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130936,c_789]) ).

tcf(c_137724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130936,c_806]) ).

tcf(c_137725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130936,c_633]) ).

tcf(c_137726,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130936,c_776]) ).

tcf(c_137727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130936,c_762]) ).

tcf(c_137728,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130936,c_761]) ).

tcf(c_137729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130936,c_642]) ).

tcf(c_137730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130936,c_774]) ).

tcf(c_137731,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130936,c_770]) ).

tcf(c_137732,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130936,c_768]) ).

tcf(c_137733,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130936,c_763]) ).

tcf(c_137813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X6),
    inference(superposition,[status(thm)],[c_125592,c_841]) ).

tcf(c_137820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_781]) ).

tcf(c_137821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_781]) ).

tcf(c_137822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_567,c_781]) ).

tcf(c_137823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_568,c_781]) ).

tcf(c_137824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_781]) ).

tcf(c_137825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,t_a),t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,c_Transitive__Closure_Ortrancl(X3,t_a)),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_781]) ).

tcf(c_137826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_781]) ).

tcf(c_137827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X3,X0,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_781]) ).

tcf(c_137828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_781]) ).

tcf(c_137829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X1,X2,X3,X4),X4,X4),X1,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_802,c_781]) ).

tcf(c_137830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X2,X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X4),tc_prod(X4,X4))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,c_Transitive__Closure_Ortrancl(X3,X4),X4),X4,X4),X3,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_803,c_781]) ).

tcf(c_137832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125781,c_781]) ).

tcf(c_137872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130936,c_781]) ).

tcf(c_137874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130925,c_781]) ).

tcf(c_137875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130457,c_781]) ).

tcf(c_137878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_781]) ).

tcf(c_137962,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_782]) ).

tcf(c_137963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_782]) ).

tcf(c_137964,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_782]) ).

tcf(c_137965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_782]) ).

tcf(c_137966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_783,c_782]) ).

tcf(c_137967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_782]) ).

tcf(c_137968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_782]) ).

tcf(c_137969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_782]) ).

tcf(c_137970,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),X0,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_782]) ).

tcf(c_137971,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_782]) ).

tcf(c_137972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_782]) ).

tcf(c_138020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_782]) ).

tcf(c_138060,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),X0,tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_137970,c_853]) ).

tcf(c_138101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_848]) ).

tcf(c_138102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X2,X2),X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_848]) ).

tcf(c_138103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_567,c_848]) ).

tcf(c_138104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X3)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_568,c_848]) ).

tcf(c_138105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_848]) ).

tcf(c_138106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,t_a),t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,c_Transitive__Closure_Ortrancl(X3,t_a)),t_a,t_a),X3,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_848]) ).

tcf(c_138107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_848]) ).

tcf(c_138108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X3,X0,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_848]) ).

tcf(c_138109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_848]) ).

tcf(c_138110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X1,X2,X3,X4),X4,X4),X1,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_802,c_848]) ).

tcf(c_138111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
      | ( X1 = X2 )
      | ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X4),tc_prod(X4,X4))
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,c_Transitive__Closure_Ortrancl(X3,X4),X4),X4,X4),X3,tc_prod(X4,X4)) ),
    inference(superposition,[status(thm)],[c_803,c_848]) ).

tcf(c_138112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_848]) ).

tcf(c_138114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126015,c_848]) ).

tcf(c_138115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126019,c_848]) ).

tcf(c_138116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126024,c_848]) ).

tcf(c_138117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126026,c_848]) ).

tcf(c_138118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126028,c_848]) ).

tcf(c_138119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126079,c_848]) ).

tcf(c_138120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126084,c_848]) ).

tcf(c_138122,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126110,c_848]) ).

tcf(c_138123,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126112,c_848]) ).

tcf(c_138124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126143,c_848]) ).

tcf(c_138125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126242,c_848]) ).

tcf(c_138126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126149,c_848]) ).

tcf(c_138127,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126155,c_848]) ).

tcf(c_138128,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126161,c_848]) ).

tcf(c_138129,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126394,c_848]) ).

tcf(c_138130,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126249,c_848]) ).

tcf(c_138131,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126289,c_848]) ).

tcf(c_138132,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126295,c_848]) ).

tcf(c_138133,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126397,c_848]) ).

tcf(c_138134,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126399,c_848]) ).

tcf(c_138135,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126404,c_848]) ).

tcf(c_138136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126413,c_848]) ).

tcf(c_138137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130451,c_848]) ).

tcf(c_138138,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126717,c_848]) ).

tcf(c_138139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126724,c_848]) ).

tcf(c_138140,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126759,c_848]) ).

tcf(c_138141,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126766,c_848]) ).

tcf(c_138142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126774,c_848]) ).

tcf(c_138143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126082,c_848]) ).

tcf(c_138144,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126781,c_848]) ).

tcf(c_138145,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126256,c_848]) ).

tcf(c_138146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126246,c_848]) ).

tcf(c_138147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126578,c_848]) ).

tcf(c_138148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126659,c_848]) ).

tcf(c_138149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126789,c_848]) ).

tcf(c_138150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126796,c_848]) ).

tcf(c_138151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126837,c_848]) ).

tcf(c_138152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130915,c_848]) ).

tcf(c_138153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130936,c_848]) ).

tcf(c_138154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128047,c_848]) ).

tcf(c_138155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130925,c_848]) ).

tcf(c_138156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130457,c_848]) ).

tcf(c_138157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X3,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X3,X2,X2),X4,X5,X6)),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130912,c_848]) ).

tcf(c_138158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X5,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135103,c_848]) ).

tcf(c_138159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_848]) ).

tcf(c_138160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_848]) ).

tcf(c_138403,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_849]) ).

tcf(c_138404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_849]) ).

tcf(c_138405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_849]) ).

tcf(c_138406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_849]) ).

tcf(c_138407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_783,c_849]) ).

tcf(c_138408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),X2,tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_849]) ).

tcf(c_138409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_849]) ).

tcf(c_138410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),X2,tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_849]) ).

tcf(c_138411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),X0,tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_849]) ).

tcf(c_138412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_849]) ).

tcf(c_138413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_849]) ).

tcf(c_138414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_849]) ).

tcf(c_138416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126015,c_849]) ).

tcf(c_138417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126019,c_849]) ).

tcf(c_138418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126024,c_849]) ).

tcf(c_138419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126026,c_849]) ).

tcf(c_138420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126028,c_849]) ).

tcf(c_138421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126079,c_849]) ).

tcf(c_138422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126084,c_849]) ).

tcf(c_138424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126110,c_849]) ).

tcf(c_138425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126112,c_849]) ).

tcf(c_138426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126143,c_849]) ).

tcf(c_138427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126242,c_849]) ).

tcf(c_138428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126149,c_849]) ).

tcf(c_138429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126155,c_849]) ).

tcf(c_138430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126161,c_849]) ).

tcf(c_138432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126249,c_849]) ).

tcf(c_138433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126289,c_849]) ).

tcf(c_138434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126295,c_849]) ).

tcf(c_138435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126397,c_849]) ).

tcf(c_138436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126399,c_849]) ).

tcf(c_138438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126413,c_849]) ).

tcf(c_138439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130451,c_849]) ).

tcf(c_138440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126717,c_849]) ).

tcf(c_138441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126724,c_849]) ).

tcf(c_138442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126759,c_849]) ).

tcf(c_138443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126766,c_849]) ).

tcf(c_138444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126774,c_849]) ).

tcf(c_138445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126082,c_849]) ).

tcf(c_138446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126781,c_849]) ).

tcf(c_138447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126256,c_849]) ).

tcf(c_138448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126246,c_849]) ).

tcf(c_138449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126578,c_849]) ).

tcf(c_138450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126659,c_849]) ).

tcf(c_138451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126789,c_849]) ).

tcf(c_138452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126796,c_849]) ).

tcf(c_138453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126837,c_849]) ).

tcf(c_138454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130915,c_849]) ).

tcf(c_138455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130936,c_849]) ).

tcf(c_138456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128047,c_849]) ).

tcf(c_138457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130925,c_849]) ).

tcf(c_138458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130457,c_849]) ).

tcf(c_138459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130912,c_849]) ).

tcf(c_138460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135103,c_849]) ).

tcf(c_138461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_849]) ).

tcf(c_138462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_849]) ).

tcf(c_138568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),X0,tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_138411,c_853]) ).

tcf(c_138847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130940,c_125973]) ).

tcf(c_138848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130940,c_125887]) ).

tcf(c_138849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130940,c_633]) ).

tcf(c_138850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130940,c_776]) ).

tcf(c_138851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130940,c_762]) ).

tcf(c_138852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130940,c_761]) ).

tcf(c_138855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130940,c_796]) ).

tcf(c_138856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130940,c_642]) ).

tcf(c_138857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130940,c_774]) ).

tcf(c_138858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130940,c_770]) ).

tcf(c_138859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130940,c_768]) ).

tcf(c_138860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130940,c_763]) ).

tcf(c_138919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130944,c_125973]) ).

tcf(c_138920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130944,c_125887]) ).

tcf(c_138921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130944,c_849]) ).

tcf(c_138922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130944,c_848]) ).

tcf(c_138924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130944,c_781]) ).

tcf(c_138925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130944,c_794]) ).

tcf(c_138926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_130944,c_784]) ).

tcf(c_138927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130944,c_800]) ).

tcf(c_138928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130944,c_786]) ).

tcf(c_138929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130944,c_789]) ).

tcf(c_138931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130944,c_806]) ).

tcf(c_138932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130944,c_633]) ).

tcf(c_138933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130944,c_776]) ).

tcf(c_138934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130944,c_762]) ).

tcf(c_138935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130944,c_761]) ).

tcf(c_138936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130944,c_642]) ).

tcf(c_138937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130944,c_774]) ).

tcf(c_138938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130944,c_770]) ).

tcf(c_138939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130944,c_768]) ).

tcf(c_138940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130944,c_763]) ).

tcf(c_139007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130947,c_125973]) ).

tcf(c_139008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_130947,c_125887]) ).

tcf(c_139009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130947,c_633]) ).

tcf(c_139010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_130947,c_776]) ).

tcf(c_139011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130947,c_762]) ).

tcf(c_139012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_130947,c_761]) ).

tcf(c_139015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130947,c_796]) ).

tcf(c_139016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130947,c_642]) ).

tcf(c_139017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130947,c_774]) ).

tcf(c_139018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_130947,c_770]) ).

tcf(c_139019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_130947,c_768]) ).

tcf(c_139020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_130947,c_763]) ).

tcf(c_139087,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130960,c_562]) ).

tcf(c_139088,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130960,c_561]) ).

tcf(c_139089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130960,c_565]) ).

tcf(c_139090,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130960,c_125973]) ).

tcf(c_139091,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130960,c_125887]) ).

tcf(c_139095,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130960,c_781]) ).

tcf(c_139096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130960,c_794]) ).

tcf(c_139097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130960,c_784]) ).

tcf(c_139098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130960,c_800]) ).

tcf(c_139099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130960,c_786]) ).

tcf(c_139102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130960,c_806]) ).

tcf(c_139103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130960,c_633]) ).

tcf(c_139104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130960,c_776]) ).

tcf(c_139105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130960,c_762]) ).

tcf(c_139107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130960,c_642]) ).

tcf(c_139108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130960,c_774]) ).

tcf(c_139109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130960,c_770]) ).

tcf(c_139110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130960,c_768]) ).

tcf(c_139111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130960,c_763]) ).

tcf(c_139145,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_139107,c_130960]) ).

tcf(c_139148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_139103,c_130960]) ).

tcf(c_139257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130967,c_562]) ).

tcf(c_139258,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130967,c_561]) ).

tcf(c_139259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130967,c_565]) ).

tcf(c_139260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130967,c_125973]) ).

tcf(c_139261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130967,c_125887]) ).

tcf(c_139262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130967,c_633]) ).

tcf(c_139263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130967,c_776]) ).

tcf(c_139264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130967,c_762]) ).

tcf(c_139268,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_130967,c_796]) ).

tcf(c_139269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130967,c_642]) ).

tcf(c_139270,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130967,c_774]) ).

tcf(c_139271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130967,c_770]) ).

tcf(c_139272,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130967,c_768]) ).

tcf(c_139273,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130967,c_763]) ).

tcf(c_139292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_139269,c_130967]) ).

tcf(c_139295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_139262,c_130967]) ).

tcf(c_139331,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130974,c_562]) ).

tcf(c_139332,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_130974,c_561]) ).

tcf(c_139333,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130974,c_565]) ).

tcf(c_139334,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130974,c_125973]) ).

tcf(c_139335,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_130974,c_125887]) ).

tcf(c_139339,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130974,c_781]) ).

tcf(c_139340,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130974,c_794]) ).

tcf(c_139341,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6))) ),
    inference(superposition,[status(thm)],[c_130974,c_784]) ).

tcf(c_139342,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130974,c_800]) ).

tcf(c_139343,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130974,c_786]) ).

tcf(c_139346,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_130974,c_806]) ).

tcf(c_139347,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130974,c_633]) ).

tcf(c_139348,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_130974,c_776]) ).

tcf(c_139349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_130974,c_762]) ).

tcf(c_139351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_130974,c_642]) ).

tcf(c_139352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_130974,c_774]) ).

tcf(c_139353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_130974,c_770]) ).

tcf(c_139354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_130974,c_768]) ).

tcf(c_139355,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_130974,c_763]) ).

tcf(c_139389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_139351,c_130974]) ).

tcf(c_139392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_139347,c_130974]) ).

tcf(c_139644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_131327,c_562]) ).

tcf(c_139645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_131327,c_561]) ).

tcf(c_139646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_131327,c_565]) ).

tcf(c_139647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_131327,c_125973]) ).

tcf(c_139648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_131327,c_125887]) ).

tcf(c_139649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131327,c_633]) ).

tcf(c_139650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_131327,c_776]) ).

tcf(c_139651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_131327,c_762]) ).

tcf(c_139655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_131327,c_796]) ).

tcf(c_139656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131327,c_642]) ).

tcf(c_139657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131327,c_774]) ).

tcf(c_139658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_131327,c_770]) ).

tcf(c_139659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_131327,c_768]) ).

tcf(c_139660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_131327,c_763]) ).

tcf(c_139679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_139656,c_131327]) ).

tcf(c_139682,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_139649,c_131327]) ).

tcf(c_139686,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131331,c_125973]) ).

tcf(c_139687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131331,c_125887]) ).

tcf(c_139688,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131331,c_849]) ).

tcf(c_139689,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131331,c_848]) ).

tcf(c_139691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131331,c_781]) ).

tcf(c_139692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131331,c_794]) ).

tcf(c_139693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131331,c_784]) ).

tcf(c_139694,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131331,c_800]) ).

tcf(c_139695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131331,c_786]) ).

tcf(c_139696,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131331,c_789]) ).

tcf(c_139698,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131331,c_806]) ).

tcf(c_139699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131331,c_633]) ).

tcf(c_139700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131331,c_776]) ).

tcf(c_139701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131331,c_762]) ).

tcf(c_139702,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131331,c_761]) ).

tcf(c_139703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131331,c_642]) ).

tcf(c_139704,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131331,c_774]) ).

tcf(c_139705,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131331,c_770]) ).

tcf(c_139706,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131331,c_768]) ).

tcf(c_139707,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131331,c_763]) ).

tcf(c_139774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131335,c_125973]) ).

tcf(c_139775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131335,c_125887]) ).

tcf(c_139776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131335,c_633]) ).

tcf(c_139777,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131335,c_776]) ).

tcf(c_139778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131335,c_762]) ).

tcf(c_139779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131335,c_761]) ).

tcf(c_139782,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_131335,c_796]) ).

tcf(c_139783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131335,c_642]) ).

tcf(c_139784,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131335,c_774]) ).

tcf(c_139785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131335,c_770]) ).

tcf(c_139786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131335,c_768]) ).

tcf(c_139787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131335,c_763]) ).

tcf(c_139813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X1,X2),X3),c_Pair(X0,X0,X2,X2)))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131349,c_125973]) ).

tcf(c_139814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_OId__on(X1,X2),X3),c_Pair(X0,X0,X2,X2)))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131349,c_125887]) ).

tcf(c_139825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X4,X4,X1,X1),c_Pair(X4,X4,X1,X1),X3,X3),X2,tc_prod(X3,X3))
      | ~ c_in(X4,X0,X1)
      | ~ c_Relation_Orefl__on(c_Relation_OId__on(X0,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_131349,c_763]) ).

tcf(c_139837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131357,c_125973]) ).

tcf(c_139838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131357,c_125887]) ).

tcf(c_139839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131357,c_849]) ).

tcf(c_139840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131357,c_848]) ).

tcf(c_139842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131357,c_781]) ).

tcf(c_139843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131357,c_794]) ).

tcf(c_139844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131357,c_784]) ).

tcf(c_139845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131357,c_800]) ).

tcf(c_139846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131357,c_786]) ).

tcf(c_139847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131357,c_789]) ).

tcf(c_139849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131357,c_806]) ).

tcf(c_139850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131357,c_633]) ).

tcf(c_139851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131357,c_776]) ).

tcf(c_139852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131357,c_762]) ).

tcf(c_139853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131357,c_761]) ).

tcf(c_139854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131357,c_642]) ).

tcf(c_139855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131357,c_774]) ).

tcf(c_139856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131357,c_770]) ).

tcf(c_139857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131357,c_768]) ).

tcf(c_139858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131357,c_763]) ).

tcf(c_139924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131379,c_125973]) ).

tcf(c_139925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131379,c_125887]) ).

tcf(c_139926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131379,c_633]) ).

tcf(c_139927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131379,c_776]) ).

tcf(c_139928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131379,c_762]) ).

tcf(c_139929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131379,c_761]) ).

tcf(c_139932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_131379,c_796]) ).

tcf(c_139933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131379,c_642]) ).

tcf(c_139934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131379,c_774]) ).

tcf(c_139935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131379,c_770]) ).

tcf(c_139936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131379,c_768]) ).

tcf(c_139937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131379,c_763]) ).

tcf(c_139958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_125593,c_841]) ).

tcf(c_139965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_634]) ).

tcf(c_139966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_634]) ).

tcf(c_139967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_634]) ).

tcf(c_139968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_634]) ).

tcf(c_139970,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Otrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_634]) ).

tcf(c_139971,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_634]) ).

tcf(c_139972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_634]) ).

tcf(c_139973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125928,c_634]) ).

tcf(c_139974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125931,c_634]) ).

tcf(c_139975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125935,c_634]) ).

tcf(c_139976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125797,c_634]) ).

tcf(c_139977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125747,c_634]) ).

tcf(c_139979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125796,c_634]) ).

tcf(c_139980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125799,c_634]) ).

tcf(c_139981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125939,c_634]) ).

tcf(c_139983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126382,c_634]) ).

tcf(c_139984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126383,c_634]) ).

tcf(c_139985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130441,c_634]) ).

tcf(c_139986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126030,c_634]) ).

tcf(c_139987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126086,c_634]) ).

tcf(c_139988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126146,c_634]) ).

tcf(c_139989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126152,c_634]) ).

tcf(c_139990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126158,c_634]) ).

tcf(c_139991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126163,c_634]) ).

tcf(c_139992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126252,c_634]) ).

tcf(c_139993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126292,c_634]) ).

tcf(c_139994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126297,c_634]) ).

tcf(c_139996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126714,c_634]) ).

tcf(c_139997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126720,c_634]) ).

tcf(c_139998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126755,c_634]) ).

tcf(c_139999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126762,c_634]) ).

tcf(c_140000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126770,c_634]) ).

tcf(c_140001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126777,c_634]) ).

tcf(c_140002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125746,c_634]) ).

tcf(c_140003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126286,c_634]) ).

tcf(c_140004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125942,c_634]) ).

tcf(c_140005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126785,c_634]) ).

tcf(c_140006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126584,c_634]) ).

tcf(c_140007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126665,c_634]) ).

tcf(c_140008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126792,c_634]) ).

tcf(c_140009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126834,c_634]) ).

tcf(c_140010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126839,c_634]) ).

tcf(c_140011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130918,c_634]) ).

tcf(c_140012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128082,c_634]) ).

tcf(c_140013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130940,c_634]) ).

tcf(c_140014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130947,c_634]) ).

tcf(c_140015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_634]) ).

tcf(c_140016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131335,c_634]) ).

tcf(c_140017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131379,c_634]) ).

tcf(c_140018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130967,c_634]) ).

tcf(c_140019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131327,c_634]) ).

tcf(c_140020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130932,c_634]) ).

tcf(c_140021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130446,c_634]) ).

tcf(c_140022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126585,c_634]) ).

tcf(c_140023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135118,c_634]) ).

tcf(c_140024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_634]) ).

tcf(c_140112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_139971,c_626]) ).

tcf(c_140238,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2))) ),
    inference(superposition,[status(thm)],[c_563,c_795]) ).

tcf(c_140239,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2))) ),
    inference(superposition,[status(thm)],[c_566,c_795]) ).

tcf(c_140240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_795]) ).

tcf(c_140241,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_795]) ).

tcf(c_140242,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_795]) ).

tcf(c_140243,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X1))
      | c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X2,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_795]) ).

tcf(c_140244,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X1,c_Relation_Oconverse(X3,X2,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_795]) ).

tcf(c_140245,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,X0,X2,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_795]) ).

tcf(c_140246,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_795]) ).

tcf(c_140247,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_795]) ).

tcf(c_140248,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_795]) ).

tcf(c_140249,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_795]) ).

tcf(c_140251,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3),X3,X3),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126015,c_795]) ).

tcf(c_140252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X4),X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126019,c_795]) ).

tcf(c_140253,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X5),X5,X5),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126024,c_795]) ).

tcf(c_140254,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126026,c_795]) ).

tcf(c_140255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126028,c_795]) ).

tcf(c_140256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126079,c_795]) ).

tcf(c_140257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126084,c_795]) ).

tcf(c_140259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126110,c_795]) ).

tcf(c_140260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126112,c_795]) ).

tcf(c_140261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126143,c_795]) ).

tcf(c_140262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126242,c_795]) ).

tcf(c_140263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126149,c_795]) ).

tcf(c_140264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126155,c_795]) ).

tcf(c_140265,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126161,c_795]) ).

tcf(c_140267,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126249,c_795]) ).

tcf(c_140268,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126289,c_795]) ).

tcf(c_140269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126295,c_795]) ).

tcf(c_140270,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126397,c_795]) ).

tcf(c_140271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126399,c_795]) ).

tcf(c_140273,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126413,c_795]) ).

tcf(c_140274,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130451,c_795]) ).

tcf(c_140275,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126717,c_795]) ).

tcf(c_140276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126724,c_795]) ).

tcf(c_140277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126759,c_795]) ).

tcf(c_140278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126766,c_795]) ).

tcf(c_140279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126774,c_795]) ).

tcf(c_140280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126082,c_795]) ).

tcf(c_140281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126781,c_795]) ).

tcf(c_140282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126256,c_795]) ).

tcf(c_140283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126246,c_795]) ).

tcf(c_140284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126578,c_795]) ).

tcf(c_140285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126659,c_795]) ).

tcf(c_140286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126789,c_795]) ).

tcf(c_140287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126796,c_795]) ).

tcf(c_140288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126837,c_795]) ).

tcf(c_140289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130915,c_795]) ).

tcf(c_140290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130936,c_795]) ).

tcf(c_140291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_128047,c_795]) ).

tcf(c_140292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130944,c_795]) ).

tcf(c_140293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131331,c_795]) ).

tcf(c_140294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131357,c_795]) ).

tcf(c_140295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130960,c_795]) ).

tcf(c_140296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130974,c_795]) ).

tcf(c_140297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130925,c_795]) ).

tcf(c_140298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130457,c_795]) ).

tcf(c_140299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130912,c_795]) ).

tcf(c_140300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X1,X5,X4,X4),X2,X3)
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_135103,c_795]) ).

tcf(c_140301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,c_Transitive__Closure_Otrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_795]) ).

tcf(c_140302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,c_Transitive__Closure_Ortrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_795]) ).

tcf(c_140559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_797]) ).

tcf(c_140560,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_797]) ).

tcf(c_140561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_797]) ).

tcf(c_140562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_797]) ).

tcf(c_140564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Otrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_797]) ).

tcf(c_140565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_797]) ).

tcf(c_140566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_797]) ).

tcf(c_140567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125928,c_797]) ).

tcf(c_140568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125931,c_797]) ).

tcf(c_140569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125935,c_797]) ).

tcf(c_140570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125797,c_797]) ).

tcf(c_140571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125747,c_797]) ).

tcf(c_140572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125794,c_797]) ).

tcf(c_140573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125796,c_797]) ).

tcf(c_140574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125799,c_797]) ).

tcf(c_140575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125939,c_797]) ).

tcf(c_140576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125952,c_797]) ).

tcf(c_140577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126382,c_797]) ).

tcf(c_140578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126383,c_797]) ).

tcf(c_140579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130441,c_797]) ).

tcf(c_140580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126030,c_797]) ).

tcf(c_140581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126086,c_797]) ).

tcf(c_140582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126146,c_797]) ).

tcf(c_140583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126152,c_797]) ).

tcf(c_140584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126158,c_797]) ).

tcf(c_140585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126163,c_797]) ).

tcf(c_140586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126252,c_797]) ).

tcf(c_140587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126292,c_797]) ).

tcf(c_140588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126297,c_797]) ).

tcf(c_140589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126409,c_797]) ).

tcf(c_140590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126714,c_797]) ).

tcf(c_140591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126720,c_797]) ).

tcf(c_140592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126755,c_797]) ).

tcf(c_140593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126762,c_797]) ).

tcf(c_140594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126770,c_797]) ).

tcf(c_140595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126777,c_797]) ).

tcf(c_140596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125746,c_797]) ).

tcf(c_140597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126286,c_797]) ).

tcf(c_140598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_125942,c_797]) ).

tcf(c_140599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126785,c_797]) ).

tcf(c_140600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126584,c_797]) ).

tcf(c_140601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126665,c_797]) ).

tcf(c_140602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126792,c_797]) ).

tcf(c_140603,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126834,c_797]) ).

tcf(c_140604,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126839,c_797]) ).

tcf(c_140605,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130918,c_797]) ).

tcf(c_140606,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128082,c_797]) ).

tcf(c_140607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130940,c_797]) ).

tcf(c_140608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130947,c_797]) ).

tcf(c_140609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_797]) ).

tcf(c_140610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131335,c_797]) ).

tcf(c_140611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131379,c_797]) ).

tcf(c_140612,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130967,c_797]) ).

tcf(c_140613,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131327,c_797]) ).

tcf(c_140614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130932,c_797]) ).

tcf(c_140615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130446,c_797]) ).

tcf(c_140616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126585,c_797]) ).

tcf(c_140617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135118,c_797]) ).

tcf(c_140618,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_698,c_797]) ).

tcf(c_140712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_140565,c_626]) ).

tcf(c_140866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_798]) ).

tcf(c_140867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_798]) ).

tcf(c_140868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_798]) ).

tcf(c_140869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_798]) ).

tcf(c_140870,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_783,c_798]) ).

tcf(c_140871,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_798]) ).

tcf(c_140872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_798]) ).

tcf(c_140873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_798]) ).

tcf(c_140874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_798]) ).

tcf(c_140875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_798]) ).

tcf(c_140876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_798]) ).

tcf(c_140929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_798]) ).

tcf(c_140969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Otrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_140874,c_853]) ).

tcf(c_140995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131383,c_125973]) ).

tcf(c_140996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131383,c_125887]) ).

tcf(c_140997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_798]) ).

tcf(c_140998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131383,c_795]) ).

tcf(c_140999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_849]) ).

tcf(c_141000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_848]) ).

tcf(c_141002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_781]) ).

tcf(c_141003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131383,c_794]) ).

tcf(c_141004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131383,c_784]) ).

tcf(c_141005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131383,c_800]) ).

tcf(c_141006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131383,c_786]) ).

tcf(c_141007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131383,c_789]) ).

tcf(c_141009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131383,c_806]) ).

tcf(c_141010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_633]) ).

tcf(c_141011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131383,c_776]) ).

tcf(c_141012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131383,c_762]) ).

tcf(c_141013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131383,c_761]) ).

tcf(c_141014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131383,c_642]) ).

tcf(c_141015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131383,c_774]) ).

tcf(c_141016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131383,c_770]) ).

tcf(c_141017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131383,c_768]) ).

tcf(c_141018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131383,c_763]) ).

tcf(c_141107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131387,c_125973]) ).

tcf(c_141108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131387,c_125887]) ).

tcf(c_141109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131387,c_633]) ).

tcf(c_141110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131387,c_776]) ).

tcf(c_141111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131387,c_762]) ).

tcf(c_141112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131387,c_761]) ).

tcf(c_141113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131387,c_797]) ).

tcf(c_141117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_131387,c_796]) ).

tcf(c_141118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131387,c_642]) ).

tcf(c_141119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131387,c_774]) ).

tcf(c_141120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131387,c_770]) ).

tcf(c_141121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131387,c_768]) ).

tcf(c_141122,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131387,c_763]) ).

tcf(c_141184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131390,c_125973]) ).

tcf(c_141185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131390,c_125887]) ).

tcf(c_141186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_798]) ).

tcf(c_141187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131390,c_795]) ).

tcf(c_141188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_849]) ).

tcf(c_141189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_848]) ).

tcf(c_141191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X1,X4,X2,X2)),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_781]) ).

tcf(c_141192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131390,c_794]) ).

tcf(c_141193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4))) ),
    inference(superposition,[status(thm)],[c_131390,c_784]) ).

tcf(c_141194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131390,c_800]) ).

tcf(c_141195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131390,c_786]) ).

tcf(c_141196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131390,c_789]) ).

tcf(c_141198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X0,X1,X3,X3)),X4),X5),X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_131390,c_806]) ).

tcf(c_141199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_633]) ).

tcf(c_141200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131390,c_776]) ).

tcf(c_141201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131390,c_762]) ).

tcf(c_141202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131390,c_761]) ).

tcf(c_141203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131390,c_642]) ).

tcf(c_141204,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131390,c_774]) ).

tcf(c_141205,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131390,c_770]) ).

tcf(c_141206,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131390,c_768]) ).

tcf(c_141207,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131390,c_763]) ).

tcf(c_141287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131392,c_125973]) ).

tcf(c_141288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_131392,c_125887]) ).

tcf(c_141289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131392,c_633]) ).

tcf(c_141290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X3)),X4),X5),X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_131392,c_776]) ).

tcf(c_141291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131392,c_762]) ).

tcf(c_141292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X3,X4,X4)),X5),X6),X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_131392,c_761]) ).

tcf(c_141293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131392,c_797]) ).

tcf(c_141297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X1,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_131392,c_796]) ).

tcf(c_141298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X5,X2,X3)),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_131392,c_642]) ).

tcf(c_141299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(X0,X3,X2,X5)),X6),X7),X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131392,c_774]) ).

tcf(c_141300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X2,X0,X3,X4)),X5),X6),X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_131392,c_770]) ).

tcf(c_141301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X6),X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_131392,c_768]) ).

tcf(c_141302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_131392,c_763]) ).

tcf(c_141362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132430,c_562]) ).

tcf(c_141363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132430,c_561]) ).

tcf(c_141364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132430,c_565]) ).

tcf(c_141365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132430,c_125973]) ).

tcf(c_141366,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132430,c_125887]) ).

tcf(c_141367,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132430,c_798]) ).

tcf(c_141372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132430,c_781]) ).

tcf(c_141373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132430,c_794]) ).

tcf(c_141374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132430,c_784]) ).

tcf(c_141375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132430,c_800]) ).

tcf(c_141376,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132430,c_786]) ).

tcf(c_141379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_132430,c_806]) ).

tcf(c_141380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132430,c_633]) ).

tcf(c_141381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132430,c_776]) ).

tcf(c_141382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132430,c_762]) ).

tcf(c_141384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132430,c_642]) ).

tcf(c_141385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132430,c_774]) ).

tcf(c_141386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132430,c_770]) ).

tcf(c_141387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132430,c_768]) ).

tcf(c_141388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132430,c_763]) ).

tcf(c_141422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_141384,c_132430]) ).

tcf(c_141427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_141380,c_132430]) ).

tcf(c_141505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132438,c_562]) ).

tcf(c_141506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132438,c_561]) ).

tcf(c_141507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132438,c_565]) ).

tcf(c_141508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132438,c_125973]) ).

tcf(c_141509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132438,c_125887]) ).

tcf(c_141510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132438,c_633]) ).

tcf(c_141511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132438,c_776]) ).

tcf(c_141512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132438,c_762]) ).

tcf(c_141518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_132438,c_796]) ).

tcf(c_141519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132438,c_642]) ).

tcf(c_141520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132438,c_774]) ).

tcf(c_141521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132438,c_770]) ).

tcf(c_141522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132438,c_768]) ).

tcf(c_141523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132438,c_763]) ).

tcf(c_141542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_141519,c_132438]) ).

tcf(c_141545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_141510,c_132438]) ).

tcf(c_141747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132446,c_562]) ).

tcf(c_141748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132446,c_561]) ).

tcf(c_141749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132446,c_565]) ).

tcf(c_141750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132446,c_125973]) ).

tcf(c_141751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132446,c_125887]) ).

tcf(c_141752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132446,c_798]) ).

tcf(c_141757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132446,c_781]) ).

tcf(c_141758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132446,c_794]) ).

tcf(c_141759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132446,c_784]) ).

tcf(c_141760,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132446,c_800]) ).

tcf(c_141761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132446,c_786]) ).

tcf(c_141764,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_132446,c_806]) ).

tcf(c_141765,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132446,c_633]) ).

tcf(c_141766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132446,c_776]) ).

tcf(c_141767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132446,c_762]) ).

tcf(c_141769,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132446,c_642]) ).

tcf(c_141770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132446,c_774]) ).

tcf(c_141771,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132446,c_770]) ).

tcf(c_141772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132446,c_768]) ).

tcf(c_141773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132446,c_763]) ).

tcf(c_141807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_141769,c_132446]) ).

tcf(c_141812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_141765,c_132446]) ).

tcf(c_141829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132453,c_562]) ).

tcf(c_141830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132453,c_561]) ).

tcf(c_141831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132453,c_565]) ).

tcf(c_141832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132453,c_125973]) ).

tcf(c_141833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132453,c_125887]) ).

tcf(c_141834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132453,c_633]) ).

tcf(c_141835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132453,c_776]) ).

tcf(c_141836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132453,c_762]) ).

tcf(c_141842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_132453,c_796]) ).

tcf(c_141843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132453,c_642]) ).

tcf(c_141844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132453,c_774]) ).

tcf(c_141845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132453,c_770]) ).

tcf(c_141846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132453,c_768]) ).

tcf(c_141847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132453,c_763]) ).

tcf(c_141866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_141843,c_132453]) ).

tcf(c_141869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_141834,c_132453]) ).

tcf(c_141896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132465,c_562]) ).

tcf(c_141897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132465,c_561]) ).

tcf(c_141898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132465,c_565]) ).

tcf(c_141899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132465,c_125973]) ).

tcf(c_141900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132465,c_125887]) ).

tcf(c_141901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132465,c_798]) ).

tcf(c_141906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132465,c_781]) ).

tcf(c_141907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132465,c_794]) ).

tcf(c_141908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132465,c_784]) ).

tcf(c_141909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132465,c_800]) ).

tcf(c_141910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132465,c_786]) ).

tcf(c_141913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_132465,c_806]) ).

tcf(c_141914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132465,c_633]) ).

tcf(c_141915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132465,c_776]) ).

tcf(c_141916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132465,c_762]) ).

tcf(c_141918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132465,c_642]) ).

tcf(c_141919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132465,c_774]) ).

tcf(c_141920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132465,c_770]) ).

tcf(c_141921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132465,c_768]) ).

tcf(c_141922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132465,c_763]) ).

tcf(c_141956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_141918,c_132465]) ).

tcf(c_141961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_141914,c_132465]) ).

tcf(c_142062,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132486,c_562]) ).

tcf(c_142063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132486,c_561]) ).

tcf(c_142064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132486,c_565]) ).

tcf(c_142065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132486,c_125973]) ).

tcf(c_142066,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132486,c_125887]) ).

tcf(c_142067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132486,c_633]) ).

tcf(c_142068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132486,c_776]) ).

tcf(c_142069,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132486,c_762]) ).

tcf(c_142075,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_132486,c_796]) ).

tcf(c_142076,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132486,c_642]) ).

tcf(c_142077,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132486,c_774]) ).

tcf(c_142078,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132486,c_770]) ).

tcf(c_142079,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132486,c_768]) ).

tcf(c_142080,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132486,c_763]) ).

tcf(c_142099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_142076,c_132486]) ).

tcf(c_142102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_142067,c_132486]) ).

tcf(c_142293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132493,c_562]) ).

tcf(c_142294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132493,c_561]) ).

tcf(c_142295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132493,c_565]) ).

tcf(c_142296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132493,c_125973]) ).

tcf(c_142297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132493,c_125887]) ).

tcf(c_142298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132493,c_798]) ).

tcf(c_142303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132493,c_781]) ).

tcf(c_142304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132493,c_794]) ).

tcf(c_142305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6))) ),
    inference(superposition,[status(thm)],[c_132493,c_784]) ).

tcf(c_142306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132493,c_800]) ).

tcf(c_142307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132493,c_786]) ).

tcf(c_142310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_132493,c_806]) ).

tcf(c_142311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132493,c_633]) ).

tcf(c_142312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132493,c_776]) ).

tcf(c_142313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132493,c_762]) ).

tcf(c_142315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132493,c_642]) ).

tcf(c_142316,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132493,c_774]) ).

tcf(c_142317,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132493,c_770]) ).

tcf(c_142318,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132493,c_768]) ).

tcf(c_142319,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132493,c_763]) ).

tcf(c_142353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_142315,c_132493]) ).

tcf(c_142358,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_142311,c_132493]) ).

tcf(c_142364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132499,c_562]) ).

tcf(c_142365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132499,c_561]) ).

tcf(c_142366,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132499,c_565]) ).

tcf(c_142367,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132499,c_125973]) ).

tcf(c_142368,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132499,c_125887]) ).

tcf(c_142369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132499,c_633]) ).

tcf(c_142370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132499,c_776]) ).

tcf(c_142371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_132499,c_762]) ).

tcf(c_142377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_132499,c_796]) ).

tcf(c_142378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132499,c_642]) ).

tcf(c_142379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132499,c_774]) ).

tcf(c_142380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132499,c_770]) ).

tcf(c_142381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132499,c_768]) ).

tcf(c_142382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132499,c_763]) ).

tcf(c_142401,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_142378,c_132499]) ).

tcf(c_142404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_142369,c_132499]) ).

tcf(c_142413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_563,c_799]) ).

tcf(c_142414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_566,c_799]) ).

tcf(c_142415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X0,X1,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_799]) ).

tcf(c_142416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X0,X1,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_799]) ).

tcf(c_142417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_799]) ).

tcf(c_142418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X1,X2,t_a),X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X1))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_799]) ).

tcf(c_142419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X0,c_Relation_Oconverse(X3,X2,X2),X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_799]) ).

tcf(c_142420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X2,t_a),v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_799]) ).

tcf(c_142421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_799]) ).

tcf(c_142422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_799]) ).

tcf(c_142423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_799]) ).

tcf(c_142424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_799]) ).

tcf(c_142426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126015,c_799]) ).

tcf(c_142427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126019,c_799]) ).

tcf(c_142428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126024,c_799]) ).

tcf(c_142429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126026,c_799]) ).

tcf(c_142430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126028,c_799]) ).

tcf(c_142431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126079,c_799]) ).

tcf(c_142432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126084,c_799]) ).

tcf(c_142434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126110,c_799]) ).

tcf(c_142435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126112,c_799]) ).

tcf(c_142436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126143,c_799]) ).

tcf(c_142437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126242,c_799]) ).

tcf(c_142438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126149,c_799]) ).

tcf(c_142439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126155,c_799]) ).

tcf(c_142440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126161,c_799]) ).

tcf(c_142442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126249,c_799]) ).

tcf(c_142443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126289,c_799]) ).

tcf(c_142444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126295,c_799]) ).

tcf(c_142445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126397,c_799]) ).

tcf(c_142446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126399,c_799]) ).

tcf(c_142448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126413,c_799]) ).

tcf(c_142449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130451,c_799]) ).

tcf(c_142450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126717,c_799]) ).

tcf(c_142451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126724,c_799]) ).

tcf(c_142452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126759,c_799]) ).

tcf(c_142453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126766,c_799]) ).

tcf(c_142454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126774,c_799]) ).

tcf(c_142455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126082,c_799]) ).

tcf(c_142456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126781,c_799]) ).

tcf(c_142457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126256,c_799]) ).

tcf(c_142458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126246,c_799]) ).

tcf(c_142459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126578,c_799]) ).

tcf(c_142460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126659,c_799]) ).

tcf(c_142461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126789,c_799]) ).

tcf(c_142462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126796,c_799]) ).

tcf(c_142463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126837,c_799]) ).

tcf(c_142464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130915,c_799]) ).

tcf(c_142465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130936,c_799]) ).

tcf(c_142466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_128047,c_799]) ).

tcf(c_142467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130944,c_799]) ).

tcf(c_142468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131331,c_799]) ).

tcf(c_142469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131357,c_799]) ).

tcf(c_142470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131383,c_799]) ).

tcf(c_142471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131390,c_799]) ).

tcf(c_142472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130960,c_799]) ).

tcf(c_142473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130974,c_799]) ).

tcf(c_142474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130925,c_799]) ).

tcf(c_142475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130457,c_799]) ).

tcf(c_142476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132430,c_799]) ).

tcf(c_142477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132446,c_799]) ).

tcf(c_142478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132465,c_799]) ).

tcf(c_142479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X1,X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132493,c_799]) ).

tcf(c_142480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130912,c_799]) ).

tcf(c_142481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X5,X1,X4,X4),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_135103,c_799]) ).

tcf(c_142482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_799]) ).

tcf(c_142483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_799]) ).

tcf(c_142670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_563,c_847]) ).

tcf(c_142671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X3,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_566,c_847]) ).

tcf(c_142672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_847]) ).

tcf(c_142673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_847]) ).

tcf(c_142674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_783,c_847]) ).

tcf(c_142675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_847]) ).

tcf(c_142676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_847]) ).

tcf(c_142677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_847]) ).

tcf(c_142678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_801,c_847]) ).

tcf(c_142679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_847]) ).

tcf(c_142680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_847]) ).

tcf(c_142683,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126015,c_847]) ).

tcf(c_142684,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126019,c_847]) ).

tcf(c_142685,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126024,c_847]) ).

tcf(c_142686,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126026,c_847]) ).

tcf(c_142687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126028,c_847]) ).

tcf(c_142688,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126079,c_847]) ).

tcf(c_142689,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126084,c_847]) ).

tcf(c_142691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126110,c_847]) ).

tcf(c_142692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126112,c_847]) ).

tcf(c_142693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126143,c_847]) ).

tcf(c_142694,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126242,c_847]) ).

tcf(c_142695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126149,c_847]) ).

tcf(c_142696,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126155,c_847]) ).

tcf(c_142697,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126161,c_847]) ).

tcf(c_142699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126249,c_847]) ).

tcf(c_142700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126289,c_847]) ).

tcf(c_142701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126295,c_847]) ).

tcf(c_142702,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126397,c_847]) ).

tcf(c_142703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126399,c_847]) ).

tcf(c_142705,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126413,c_847]) ).

tcf(c_142706,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130451,c_847]) ).

tcf(c_142707,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126717,c_847]) ).

tcf(c_142708,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126724,c_847]) ).

tcf(c_142709,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126759,c_847]) ).

tcf(c_142710,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126766,c_847]) ).

tcf(c_142711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126774,c_847]) ).

tcf(c_142712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126082,c_847]) ).

tcf(c_142713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126781,c_847]) ).

tcf(c_142714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126256,c_847]) ).

tcf(c_142715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126246,c_847]) ).

tcf(c_142716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126578,c_847]) ).

tcf(c_142717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126659,c_847]) ).

tcf(c_142718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126789,c_847]) ).

tcf(c_142719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126796,c_847]) ).

tcf(c_142720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126837,c_847]) ).

tcf(c_142721,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130915,c_847]) ).

tcf(c_142722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130936,c_847]) ).

tcf(c_142723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128047,c_847]) ).

tcf(c_142724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130944,c_847]) ).

tcf(c_142725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131331,c_847]) ).

tcf(c_142726,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131357,c_847]) ).

tcf(c_142727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_847]) ).

tcf(c_142728,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X4,X0,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_847]) ).

tcf(c_142729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130960,c_847]) ).

tcf(c_142730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130974,c_847]) ).

tcf(c_142731,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130925,c_847]) ).

tcf(c_142732,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130457,c_847]) ).

tcf(c_142733,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132430,c_847]) ).

tcf(c_142734,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132446,c_847]) ).

tcf(c_142735,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132465,c_847]) ).

tcf(c_142736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132493,c_847]) ).

tcf(c_142737,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X3,X0,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130912,c_847]) ).

tcf(c_142738,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135103,c_847]) ).

tcf(c_142739,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_847]) ).

tcf(c_142740,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_847]) ).

tcf(c_142843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ( X2 = X3 )
      | ~ c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X3,X1),X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(light_normalisation,[status(thm)],[c_142678,c_853]) ).

tcf(c_143156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X3,X3),X2,tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_563,c_631]) ).

tcf(c_143157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X2,X3),X3),X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X2,X3),X1,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X3,X3),X2,tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_566,c_631]) ).

tcf(c_143158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,X0,X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X0,X1,X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_631]) ).

tcf(c_143159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,X0,X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X0,X1,X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_631]) ).

tcf(c_143160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_631]) ).

tcf(c_143161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,X1,X2,t_a),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,X1,X2,t_a),t_a,t_a),X2,tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X1))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_631]) ).

tcf(c_143162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X0,c_Relation_Oconverse(X3,X2,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X0,c_Relation_Oconverse(X3,X2,X2),X2),X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_631]) ).

tcf(c_143163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X2,t_a),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X2,t_a),t_a,t_a),X2,tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_631]) ).

tcf(c_143164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_631]) ).

tcf(c_143165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_631]) ).

tcf(c_143166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_631]) ).

tcf(c_143167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_631]) ).

tcf(c_143169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X3),X3,X3),hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126015,c_631]) ).

tcf(c_143170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X4),X4,X4),hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126019,c_631]) ).

tcf(c_143171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X5),X5,X5),hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126024,c_631]) ).

tcf(c_143172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),X3,X3),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126026,c_631]) ).

tcf(c_143173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X3),X3,X3),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126028,c_631]) ).

tcf(c_143174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),X4,X4),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126079,c_631]) ).

tcf(c_143175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X4),X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126084,c_631]) ).

tcf(c_143177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),X5,X5),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126110,c_631]) ).

tcf(c_143178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126112,c_631]) ).

tcf(c_143179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X5),X5,X5),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126143,c_631]) ).

tcf(c_143180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126242,c_631]) ).

tcf(c_143181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126149,c_631]) ).

tcf(c_143182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126155,c_631]) ).

tcf(c_143183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126161,c_631]) ).

tcf(c_143185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126249,c_631]) ).

tcf(c_143186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126289,c_631]) ).

tcf(c_143187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126295,c_631]) ).

tcf(c_143188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126397,c_631]) ).

tcf(c_143189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126399,c_631]) ).

tcf(c_143191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126413,c_631]) ).

tcf(c_143192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130451,c_631]) ).

tcf(c_143193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126717,c_631]) ).

tcf(c_143194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126724,c_631]) ).

tcf(c_143195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126759,c_631]) ).

tcf(c_143196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126766,c_631]) ).

tcf(c_143197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126774,c_631]) ).

tcf(c_143198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X4,X4),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126082,c_631]) ).

tcf(c_143199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126781,c_631]) ).

tcf(c_143200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126256,c_631]) ).

tcf(c_143201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126246,c_631]) ).

tcf(c_143202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126578,c_631]) ).

tcf(c_143203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126659,c_631]) ).

tcf(c_143204,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126789,c_631]) ).

tcf(c_143205,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126796,c_631]) ).

tcf(c_143206,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126837,c_631]) ).

tcf(c_143207,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130915,c_631]) ).

tcf(c_143208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130936,c_631]) ).

tcf(c_143209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X6,X6),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_128047,c_631]) ).

tcf(c_143210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130944,c_631]) ).

tcf(c_143211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131331,c_631]) ).

tcf(c_143212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131357,c_631]) ).

tcf(c_143213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131383,c_631]) ).

tcf(c_143214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X3,X1,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131390,c_631]) ).

tcf(c_143215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130960,c_631]) ).

tcf(c_143216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130974,c_631]) ).

tcf(c_143217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130925,c_631]) ).

tcf(c_143218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130457,c_631]) ).

tcf(c_143219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132430,c_631]) ).

tcf(c_143220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132446,c_631]) ).

tcf(c_143221,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132465,c_631]) ).

tcf(c_143222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132493,c_631]) ).

tcf(c_143223,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),X3),X3,X3),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X2,X1,X3,X3),X4,X5,X6)),X5,X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130912,c_631]) ).

tcf(c_143224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X5,X1,X4,X4),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X4,X4),c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_135103,c_631]) ).

tcf(c_143225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,c_Transitive__Closure_Otrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_631]) ).

tcf(c_143226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X4,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X4,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_631]) ).

tcf(c_143515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2))) ),
    inference(superposition,[status(thm)],[c_563,c_632]) ).

tcf(c_143516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2),X1,X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2))) ),
    inference(superposition,[status(thm)],[c_566,c_632]) ).

tcf(c_143517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_632]) ).

tcf(c_143518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X1,X2),X2,X2),X1,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2)))
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_632]) ).

tcf(c_143519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_632]) ).

tcf(c_143520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X2,t_a),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X2,t_a),t_a,t_a),X2,tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a))))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_632]) ).

tcf(c_143521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X1,c_Relation_Oconverse(X3,X2,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X1,c_Relation_Oconverse(X3,X2,X2),X2),X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X1))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_632]) ).

tcf(c_143522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X3,X0,X2,t_a),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X3,X0,X2,t_a),t_a,t_a),X2,tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X3,X0))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_632]) ).

tcf(c_143523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_632]) ).

tcf(c_143524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_632]) ).

tcf(c_143525,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_632]) ).

tcf(c_143526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,X3,X2),X2,X2),X3,tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_632]) ).

tcf(c_143528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X3),X3,X3),hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126015,c_632]) ).

tcf(c_143529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X4),X4,X4),hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126019,c_632]) ).

tcf(c_143530,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X5),X5,X5),hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126024,c_632]) ).

tcf(c_143531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),X3,X3),c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126026,c_632]) ).

tcf(c_143532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X3),X3,X3),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126028,c_632]) ).

tcf(c_143533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),X4,X4),c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126079,c_632]) ).

tcf(c_143534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X4),X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126084,c_632]) ).

tcf(c_143536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),X5,X5),c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126110,c_632]) ).

tcf(c_143537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126112,c_632]) ).

tcf(c_143538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X5),X5,X5),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126143,c_632]) ).

tcf(c_143539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126242,c_632]) ).

tcf(c_143540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126149,c_632]) ).

tcf(c_143541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126155,c_632]) ).

tcf(c_143542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126161,c_632]) ).

tcf(c_143544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126249,c_632]) ).

tcf(c_143545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126289,c_632]) ).

tcf(c_143546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126295,c_632]) ).

tcf(c_143547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126397,c_632]) ).

tcf(c_143548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126399,c_632]) ).

tcf(c_143550,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126413,c_632]) ).

tcf(c_143551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130451,c_632]) ).

tcf(c_143552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126717,c_632]) ).

tcf(c_143553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126724,c_632]) ).

tcf(c_143554,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126759,c_632]) ).

tcf(c_143555,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126766,c_632]) ).

tcf(c_143556,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126774,c_632]) ).

tcf(c_143557,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X4,X4),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126082,c_632]) ).

tcf(c_143558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126781,c_632]) ).

tcf(c_143559,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126256,c_632]) ).

tcf(c_143560,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126246,c_632]) ).

tcf(c_143561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126578,c_632]) ).

tcf(c_143562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126659,c_632]) ).

tcf(c_143563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126789,c_632]) ).

tcf(c_143564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126796,c_632]) ).

tcf(c_143565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_126837,c_632]) ).

tcf(c_143566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130915,c_632]) ).

tcf(c_143567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130936,c_632]) ).

tcf(c_143568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X6,X6),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_128047,c_632]) ).

tcf(c_143569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130944,c_632]) ).

tcf(c_143570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131331,c_632]) ).

tcf(c_143571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131357,c_632]) ).

tcf(c_143572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131383,c_632]) ).

tcf(c_143573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),X4),X4,X4),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X2),c_Pair(X1,X3,X4,X4)),X5),X6),X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_131390,c_632]) ).

tcf(c_143574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130960,c_632]) ).

tcf(c_143575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130974,c_632]) ).

tcf(c_143576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130925,c_632]) ).

tcf(c_143577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130457,c_632]) ).

tcf(c_143578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132430,c_632]) ).

tcf(c_143579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132446,c_632]) ).

tcf(c_143580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132465,c_632]) ).

tcf(c_143581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),X6),X6,X6),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132493,c_632]) ).

tcf(c_143582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),X3),X3,X3),c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X1,X2,X3,X3),X4,X5,X6)),X5,X6),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_130912,c_632]) ).

tcf(c_143583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X1,X5,X4,X4),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X4,X4),c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_135103,c_632]) ).

tcf(c_143584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,c_Transitive__Closure_Otrancl(X3,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,c_Transitive__Closure_Otrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_632]) ).

tcf(c_143585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X1))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X4,X0,c_Transitive__Closure_Ortrancl(X3,X2),X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X4,X0,c_Transitive__Closure_Ortrancl(X3,X2),X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_632]) ).

tcf(c_143925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132506,c_562]) ).

tcf(c_143926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_132506,c_561]) ).

tcf(c_143927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132506,c_565]) ).

tcf(c_143928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132506,c_125973]) ).

tcf(c_143929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_132506,c_125887]) ).

tcf(c_143930,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132506,c_632]) ).

tcf(c_143931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132506,c_631]) ).

tcf(c_143934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132506,c_798]) ).

tcf(c_143939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132506,c_781]) ).

tcf(c_143940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_132506,c_794]) ).

tcf(c_143941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_132506,c_784]) ).

tcf(c_143942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132506,c_800]) ).

tcf(c_143943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_132506,c_786]) ).

tcf(c_143946,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_132506,c_806]) ).

tcf(c_143947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132506,c_633]) ).

tcf(c_143948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_132506,c_776]) ).

tcf(c_143949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_132506,c_762]) ).

tcf(c_143951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_132506,c_642]) ).

tcf(c_143952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_132506,c_774]) ).

tcf(c_143953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_132506,c_770]) ).

tcf(c_143954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_132506,c_768]) ).

tcf(c_143955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_132506,c_763]) ).

tcf(c_143989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_143951,c_132506]) ).

tcf(c_143994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_143947,c_132506]) ).

tcf(c_144033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134095,c_562]) ).

tcf(c_144034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134095,c_561]) ).

tcf(c_144035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134095,c_565]) ).

tcf(c_144036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134095,c_125973]) ).

tcf(c_144037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134095,c_125887]) ).

tcf(c_144038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134095,c_633]) ).

tcf(c_144039,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134095,c_776]) ).

tcf(c_144040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134095,c_762]) ).

tcf(c_144046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_134095,c_796]) ).

tcf(c_144047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134095,c_642]) ).

tcf(c_144048,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134095,c_774]) ).

tcf(c_144049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134095,c_770]) ).

tcf(c_144050,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134095,c_768]) ).

tcf(c_144051,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134095,c_763]) ).

tcf(c_144070,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144047,c_134095]) ).

tcf(c_144073,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144038,c_134095]) ).

tcf(c_144133,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134102,c_562]) ).

tcf(c_144134,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134102,c_561]) ).

tcf(c_144135,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134102,c_565]) ).

tcf(c_144136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134102,c_125973]) ).

tcf(c_144137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134102,c_125887]) ).

tcf(c_144138,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134102,c_632]) ).

tcf(c_144139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134102,c_631]) ).

tcf(c_144142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134102,c_798]) ).

tcf(c_144147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134102,c_781]) ).

tcf(c_144148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_134102,c_794]) ).

tcf(c_144149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_134102,c_784]) ).

tcf(c_144150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134102,c_800]) ).

tcf(c_144151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134102,c_786]) ).

tcf(c_144154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_134102,c_806]) ).

tcf(c_144155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134102,c_633]) ).

tcf(c_144156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134102,c_776]) ).

tcf(c_144157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134102,c_762]) ).

tcf(c_144159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134102,c_642]) ).

tcf(c_144160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134102,c_774]) ).

tcf(c_144161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134102,c_770]) ).

tcf(c_144162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134102,c_768]) ).

tcf(c_144163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134102,c_763]) ).

tcf(c_144197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144159,c_134102]) ).

tcf(c_144202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144155,c_134102]) ).

tcf(c_144219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134109,c_562]) ).

tcf(c_144220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134109,c_561]) ).

tcf(c_144221,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134109,c_565]) ).

tcf(c_144222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134109,c_125973]) ).

tcf(c_144223,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134109,c_125887]) ).

tcf(c_144224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134109,c_633]) ).

tcf(c_144225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134109,c_776]) ).

tcf(c_144226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134109,c_762]) ).

tcf(c_144232,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_134109,c_796]) ).

tcf(c_144233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134109,c_642]) ).

tcf(c_144234,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134109,c_774]) ).

tcf(c_144235,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134109,c_770]) ).

tcf(c_144236,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134109,c_768]) ).

tcf(c_144237,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134109,c_763]) ).

tcf(c_144256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144233,c_134109]) ).

tcf(c_144259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144224,c_134109]) ).

tcf(c_144356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134143,c_562]) ).

tcf(c_144357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134143,c_561]) ).

tcf(c_144358,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134143,c_565]) ).

tcf(c_144359,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134143,c_125973]) ).

tcf(c_144360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134143,c_125887]) ).

tcf(c_144361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134143,c_632]) ).

tcf(c_144362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134143,c_631]) ).

tcf(c_144365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134143,c_798]) ).

tcf(c_144370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134143,c_781]) ).

tcf(c_144371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_134143,c_794]) ).

tcf(c_144372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_134143,c_784]) ).

tcf(c_144373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134143,c_800]) ).

tcf(c_144374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134143,c_786]) ).

tcf(c_144377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_134143,c_806]) ).

tcf(c_144378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134143,c_633]) ).

tcf(c_144379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134143,c_776]) ).

tcf(c_144380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134143,c_762]) ).

tcf(c_144382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134143,c_642]) ).

tcf(c_144383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134143,c_774]) ).

tcf(c_144384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134143,c_770]) ).

tcf(c_144385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134143,c_768]) ).

tcf(c_144386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134143,c_763]) ).

tcf(c_144420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144382,c_134143]) ).

tcf(c_144425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144378,c_134143]) ).

tcf(c_144451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134150,c_562]) ).

tcf(c_144452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134150,c_561]) ).

tcf(c_144453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134150,c_565]) ).

tcf(c_144454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134150,c_125973]) ).

tcf(c_144455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134150,c_125887]) ).

tcf(c_144456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134150,c_633]) ).

tcf(c_144457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134150,c_776]) ).

tcf(c_144458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134150,c_762]) ).

tcf(c_144464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_134150,c_796]) ).

tcf(c_144465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134150,c_642]) ).

tcf(c_144466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134150,c_774]) ).

tcf(c_144467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134150,c_770]) ).

tcf(c_144468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134150,c_768]) ).

tcf(c_144469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134150,c_763]) ).

tcf(c_144488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144465,c_134150]) ).

tcf(c_144491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144456,c_134150]) ).

tcf(c_144609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134166,c_562]) ).

tcf(c_144610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134166,c_561]) ).

tcf(c_144611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134166,c_565]) ).

tcf(c_144612,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134166,c_125973]) ).

tcf(c_144613,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134166,c_125887]) ).

tcf(c_144614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134166,c_632]) ).

tcf(c_144615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6),X6,X6),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),tc_prod(X6,X6))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134166,c_631]) ).

tcf(c_144618,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134166,c_798]) ).

tcf(c_144623,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134166,c_781]) ).

tcf(c_144624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_134166,c_794]) ).

tcf(c_144625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6))) ),
    inference(superposition,[status(thm)],[c_134166,c_784]) ).

tcf(c_144626,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134166,c_800]) ).

tcf(c_144627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X7))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_134166,c_786]) ).

tcf(c_144630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X5),X3,X3),X6,X6),X6)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_134166,c_806]) ).

tcf(c_144631,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134166,c_633]) ).

tcf(c_144632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134166,c_776]) ).

tcf(c_144633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134166,c_762]) ).

tcf(c_144635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134166,c_642]) ).

tcf(c_144636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134166,c_774]) ).

tcf(c_144637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134166,c_770]) ).

tcf(c_144638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134166,c_768]) ).

tcf(c_144639,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134166,c_763]) ).

tcf(c_144673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144635,c_134166]) ).

tcf(c_144678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144631,c_134166]) ).

tcf(c_144686,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134850,c_562]) ).

tcf(c_144687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_134850,c_561]) ).

tcf(c_144688,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134850,c_565]) ).

tcf(c_144689,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134850,c_125973]) ).

tcf(c_144690,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5),X6)),
    inference(superposition,[status(thm)],[c_134850,c_125887]) ).

tcf(c_144691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134850,c_633]) ).

tcf(c_144692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X6) ),
    inference(superposition,[status(thm)],[c_134850,c_776]) ).

tcf(c_144693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6) ),
    inference(superposition,[status(thm)],[c_134850,c_762]) ).

tcf(c_144699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_134850,c_796]) ).

tcf(c_144700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_134850,c_642]) ).

tcf(c_144701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_134850,c_774]) ).

tcf(c_144702,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_134850,c_770]) ).

tcf(c_144703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6,X7),X6),
    inference(superposition,[status(thm)],[c_134850,c_768]) ).

tcf(c_144704,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_134850,c_763]) ).

tcf(c_144723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144700,c_134850]) ).

tcf(c_144726,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_144691,c_134850]) ).

tcf(c_144819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5),
    inference(superposition,[status(thm)],[c_135400,c_841]) ).

tcf(c_144826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1,X1),X4))
      | ~ c_in(X4,c_Wellfounded_Oacc(X3,t_a),t_a)
      | ~ c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1,X1),X3),X2,X1) ),
    inference(superposition,[status(thm)],[c_135471,c_517]) ).

tcf(c_144827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1,X1),X5))
      | ~ c_in(X5,c_Wellfounded_Oacc(X3,X4),X4)
      | ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1,X1),X3,X4),X2,X1) ),
    inference(superposition,[status(thm)],[c_135471,c_537]) ).

tcf(c_144828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X1,X2,X2),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_135471,c_841]) ).

tcf(c_144841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),X2,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),X3) ),
    inference(superposition,[status(thm)],[c_563,c_136744]) ).

tcf(c_144842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),X2,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),X3) ),
    inference(superposition,[status(thm)],[c_566,c_136744]) ).

tcf(c_144843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),X3)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_136744]) ).

tcf(c_144844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),X3)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_136744]) ).

tcf(c_144845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_136744]) ).

tcf(c_144846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),X3)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_136744]) ).

tcf(c_144847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X4)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_136744]) ).

tcf(c_144848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),X3)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_136744]) ).

tcf(c_144849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_136744]) ).

tcf(c_144850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_136744]) ).

tcf(c_144851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X3,X2),X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_136744]) ).

tcf(c_144852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),X3)
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_844,c_136744]) ).

tcf(c_144914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X3)
      | ~ c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_136744]) ).

tcf(c_144915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X3)
      | ~ c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_136744]) ).

tcf(c_144983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X0,X2),X3) ),
    inference(superposition,[status(thm)],[c_563,c_144852]) ).

tcf(c_144984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X0,X2),X3) ),
    inference(superposition,[status(thm)],[c_566,c_144852]) ).

tcf(c_144985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,X1,X2,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),X3)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_567,c_144852]) ).

tcf(c_144986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,X1,X2,X2),X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),X3)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_568,c_144852]) ).

tcf(c_144987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X3)
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_603,c_144852]) ).

tcf(c_144988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X4)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_641,c_144852]) ).

tcf(c_144989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X2,X0,X3,X3),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(X4,X1,X3,X3),X3),X5)
      | ~ c_in(X2,X4,X3)
      | ~ c_in(X0,hAPP(X1,X2),X3) ),
    inference(superposition,[status(thm)],[c_778,c_144852]) ).

tcf(c_144990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_144852]) ).

tcf(c_144991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),X3)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_144852]) ).

tcf(c_144992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X2),X4)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_144852]) ).

tcf(c_144993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),X3)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_144852]) ).

tcf(c_144994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_144852]) ).

tcf(c_144995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X0,X1,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_802,c_144852]) ).

tcf(c_144996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),X4)
      | ( X0 = X1 )
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_803,c_144852]) ).

tcf(c_145010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_125952,c_144852]) ).

tcf(c_145011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126382,c_144852]) ).

tcf(c_145012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126383,c_144852]) ).

tcf(c_145013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130441,c_144852]) ).

tcf(c_145035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126394,c_144852]) ).

tcf(c_145042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126397,c_144852]) ).

tcf(c_145043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126399,c_144852]) ).

tcf(c_145044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126404,c_144852]) ).

tcf(c_145045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126409,c_144852]) ).

tcf(c_145046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126413,c_144852]) ).

tcf(c_145047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130451,c_144852]) ).

tcf(c_145048,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126714,c_144852]) ).

tcf(c_145049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126717,c_144852]) ).

tcf(c_145050,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126720,c_144852]) ).

tcf(c_145051,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126724,c_144852]) ).

tcf(c_145052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126755,c_144852]) ).

tcf(c_145053,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126759,c_144852]) ).

tcf(c_145054,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126762,c_144852]) ).

tcf(c_145055,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126766,c_144852]) ).

tcf(c_145056,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126770,c_144852]) ).

tcf(c_145057,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126774,c_144852]) ).

tcf(c_145058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126777,c_144852]) ).

tcf(c_145064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126781,c_144852]) ).

tcf(c_145071,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126785,c_144852]) ).

tcf(c_145078,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126789,c_144852]) ).

tcf(c_145079,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126792,c_144852]) ).

tcf(c_145080,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126796,c_144852]) ).

tcf(c_145081,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126834,c_144852]) ).

tcf(c_145082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126837,c_144852]) ).

tcf(c_145083,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126839,c_144852]) ).

tcf(c_145084,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130915,c_144852]) ).

tcf(c_145087,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130918,c_144852]) ).

tcf(c_145088,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130936,c_144852]) ).

tcf(c_145089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128047,c_144852]) ).

tcf(c_145090,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128082,c_144852]) ).

tcf(c_145091,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130940,c_144852]) ).

tcf(c_145092,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X1,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X4)
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128590,c_144852]) ).

tcf(c_145093,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X3,X4),X5),X6),
    inference(superposition,[status(thm)],[c_129469,c_144852]) ).

tcf(c_145094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_129474,c_144852]) ).

tcf(c_145095,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_129480,c_144852]) ).

tcf(c_145096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_129487,c_144852]) ).

tcf(c_145097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_129493,c_144852]) ).

tcf(c_145098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130944,c_144852]) ).

tcf(c_145099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_129942,c_144852]) ).

tcf(c_145100,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_129951,c_144852]) ).

tcf(c_145101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130947,c_144852]) ).

tcf(c_145102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X1,X2),X2),X3),X4)
      | ~ c_in(X0,X1,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130430,c_144852]) ).

tcf(c_145103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X0,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(X1,X2),X3),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_131349,c_144852]) ).

tcf(c_145104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131331,c_144852]) ).

tcf(c_145105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131335,c_144852]) ).

tcf(c_145106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131357,c_144852]) ).

tcf(c_145107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131379,c_144852]) ).

tcf(c_145108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131383,c_144852]) ).

tcf(c_145109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131387,c_144852]) ).

tcf(c_145110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131390,c_144852]) ).

tcf(c_145111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),X0),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131392,c_144852]) ).

tcf(c_145112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130960,c_144852]) ).

tcf(c_145113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130967,c_144852]) ).

tcf(c_145114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130974,c_144852]) ).

tcf(c_145115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_131327,c_144852]) ).

tcf(c_145116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130925,c_144852]) ).

tcf(c_145117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130932,c_144852]) ).

tcf(c_145118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130457,c_144852]) ).

tcf(c_145119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_130446,c_144852]) ).

tcf(c_145120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132430,c_144852]) ).

tcf(c_145121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132438,c_144852]) ).

tcf(c_145122,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132446,c_144852]) ).

tcf(c_145123,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132453,c_144852]) ).

tcf(c_145124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132465,c_144852]) ).

tcf(c_145125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132486,c_144852]) ).

tcf(c_145126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132493,c_144852]) ).

tcf(c_145127,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132499,c_144852]) ).

tcf(c_145128,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_130912,c_144852]) ).

tcf(c_145129,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126585,c_144852]) ).

tcf(c_145130,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_132506,c_144852]) ).

tcf(c_145131,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134095,c_144852]) ).

tcf(c_145132,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134102,c_144852]) ).

tcf(c_145133,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134109,c_144852]) ).

tcf(c_145135,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_135103,c_144852]) ).

tcf(c_145136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_135118,c_144852]) ).

tcf(c_145137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134143,c_144852]) ).

tcf(c_145138,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134150,c_144852]) ).

tcf(c_145139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134166,c_144852]) ).

tcf(c_145140,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),X6),X7),
    inference(superposition,[status(thm)],[c_134850,c_144852]) ).

tcf(c_145141,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_97184,c_144852]) ).

tcf(c_145142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X6),
    inference(superposition,[status(thm)],[c_97186,c_144852]) ).

tcf(c_145143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X2,X3),X5),X6),
    inference(superposition,[status(thm)],[c_97187,c_144852]) ).

tcf(c_145144,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_97192,c_144852]) ).

tcf(c_145381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(X0,X3,iPr_def_11,iPr_def_12),c_Pair(X1,X4,iPr_def_11,iPr_def_12),iPr_def_13,iPr_def_13),c_Wellfounded_Olex__prod(X2,X5,iPr_def_11,iPr_def_12),tc_prod(iPr_def_13,iPr_def_13))
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_11),X2,tc_prod(iPr_def_11,iPr_def_11)) ),
    inference(superposition,[status(thm)],[c_7266,c_812]) ).

tcf(c_145385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X0,X4,X2,X5),c_Pair(X1,X6,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5)),c_Transitive__Closure_Ortrancl(c_Wellfounded_Olex__prod(X3,X7,X2,X5),tc_prod(X2,X5)),X8)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_144852]) ).

tcf(c_145386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Olex__prod(X3,X4,X2,X5),tc_prod(X2,X5)),c_Pair(c_Pair(X0,X6,X2,X5),c_Pair(X1,X7,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5))))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_125973]) ).

tcf(c_145387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Olex__prod(X3,X4,X2,X5),tc_prod(X2,X5)),c_Pair(c_Pair(X0,X6,X2,X5),c_Pair(X1,X7,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5))))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_125887]) ).

tcf(c_145388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X7,X8,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Transitive__Closure_Otrancl(c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)))
      | ~ c_in(c_Pair(X7,X0,X2,X2),X5,tc_prod(X2,X2))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_812,c_633]) ).

tcf(c_145389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X6,X7,X2,X3),c_Wellfounded_Oacc(c_Wellfounded_Olex__prod(X4,X5,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3))
      | ~ c_in(c_Pair(X6,X0,X2,X2),X4,tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Wellfounded_Olex__prod(X4,X5,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_812,c_776]) ).

tcf(c_145390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X7,X2,X6),X4,tc_prod(X2,X6))
      | ~ c_Relation_Orefl__on(X4,c_Wellfounded_Olex__prod(X3,X5,X2,X6),tc_prod(X2,X6))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_762]) ).

tcf(c_145391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X2,X6),X4,tc_prod(X2,X6))
      | ~ c_Relation_Orefl__on(X4,c_Wellfounded_Olex__prod(X3,X5,X2,X6),tc_prod(X2,X6))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_761]) ).

tcf(c_145392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( c_Pair(X7,X8,X2,X3) = X4 )
      | ~ c_in(c_Pair(X0,X7,X2,X2),X5,tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_812,c_642]) ).

tcf(c_145393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X1,X7,X2,X5),c_Relation_OImage(c_Wellfounded_Olex__prod(X3,X8,X2,X5),X6,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5))
      | ~ c_in(c_Pair(X0,X4,X2,X5),X6,tc_prod(X2,X5))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_774]) ).

tcf(c_145394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X4,X2,X5),c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Olex__prod(X3,X6,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_770]) ).

tcf(c_145395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X4,X2,X5),c_Relation_ODomain(c_Wellfounded_Olex__prod(X3,X6,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_768]) ).

tcf(c_145396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(X5,X7,X2,X3),c_Pair(X6,X8,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Pair(c_Pair(X5,X7,X2,X3),c_Pair(X6,X8,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))),X4,tc_prod(tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))))
      | ~ c_in(c_Pair(X5,X6,X2,X2),X0,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Olex__prod(X0,X1,X2,X3),X4,tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_812,c_763]) ).

tcf(c_145397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Olex__prod(X3,X4,X2,X5),c_Pair(c_Pair(X0,X6,X2,X5),c_Pair(X1,X7,X2,X5),tc_prod(X2,X5),tc_prod(X2,X5))))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_812,c_840]) ).

tcf(c_145438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X3,X0,iPr_def_11,iPr_def_12),c_Pair(X3,X1,iPr_def_11,iPr_def_12),iPr_def_13,iPr_def_13),c_Wellfounded_Olex__prod(X4,X2,iPr_def_11,iPr_def_12),tc_prod(iPr_def_13,iPr_def_13))
      | ~ c_in(c_Pair(X0,X1,iPr_def_12,iPr_def_12),X2,tc_prod(iPr_def_12,iPr_def_12)) ),
    inference(superposition,[status(thm)],[c_7266,c_813]) ).

tcf(c_145442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X4,X0,X5,X2),c_Pair(X4,X1,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2)),c_Transitive__Closure_Ortrancl(c_Wellfounded_Olex__prod(X6,X3,X5,X2),tc_prod(X5,X2)),X7)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_144852]) ).

tcf(c_145443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Olex__prod(X4,X3,X5,X2),tc_prod(X5,X2)),c_Pair(c_Pair(X6,X0,X5,X2),c_Pair(X6,X1,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2))))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_125973]) ).

tcf(c_145444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Olex__prod(X4,X3,X5,X2),tc_prod(X5,X2)),c_Pair(c_Pair(X6,X0,X5,X2),c_Pair(X6,X1,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2))))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_125887]) ).

tcf(c_145445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,X7,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Transitive__Closure_Otrancl(c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)))
      | ~ c_in(c_Pair(X7,X1,X3,X3),X6,tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_813,c_633]) ).

tcf(c_145446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X3),c_Wellfounded_Oacc(c_Wellfounded_Olex__prod(X4,X5,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3))
      | ~ c_in(c_Pair(X6,X1,X3,X3),X5,tc_prod(X3,X3))
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Wellfounded_Olex__prod(X4,X5,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_813,c_776]) ).

tcf(c_145447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X6,X2),X4,tc_prod(X6,X2))
      | ~ c_Relation_Orefl__on(X4,c_Wellfounded_Olex__prod(X5,X3,X6,X2),tc_prod(X6,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_762]) ).

tcf(c_145448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X6,X2),X4,tc_prod(X6,X2))
      | ~ c_Relation_Orefl__on(X4,c_Wellfounded_Olex__prod(X5,X3,X6,X2),tc_prod(X6,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_761]) ).

tcf(c_145449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(X0,X7,X2,X3) = X4 )
      | ~ c_in(c_Pair(X1,X7,X3,X3),X6,tc_prod(X3,X3))
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Olex__prod(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_813,c_642]) ).

tcf(c_145450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X5,X2),c_Relation_OImage(c_Wellfounded_Olex__prod(X7,X3,X5,X2),X6,tc_prod(X5,X2),tc_prod(X5,X2)),tc_prod(X5,X2))
      | ~ c_in(c_Pair(X4,X0,X5,X2),X6,tc_prod(X5,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_774]) ).

tcf(c_145451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X5,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Olex__prod(X6,X3,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2)),tc_prod(X5,X2),tc_prod(X5,X2)),tc_prod(X5,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_770]) ).

tcf(c_145452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X0,X5,X2),c_Relation_ODomain(c_Wellfounded_Olex__prod(X6,X3,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2)),tc_prod(X5,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_768]) ).

tcf(c_145453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(X7,X5,X2,X3),c_Pair(X7,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Pair(c_Pair(X7,X5,X2,X3),c_Pair(X7,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))),X4,tc_prod(tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))))
      | ~ c_in(c_Pair(X5,X6,X3,X3),X1,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Olex__prod(X0,X1,X2,X3),X4,tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_813,c_763]) ).

tcf(c_145454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Olex__prod(X4,X3,X5,X2),c_Pair(c_Pair(X6,X0,X5,X2),c_Pair(X6,X1,X5,X2),tc_prod(X5,X2),tc_prod(X5,X2))))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_813,c_840]) ).

tcf(c_145518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X2,iPr_def_11,iPr_def_11),X4,tc_prod(iPr_def_11,iPr_def_11))
      | ( X0 = X2 )
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),c_Pair(X2,X3,iPr_def_11,iPr_def_12),iPr_def_13,iPr_def_13),c_Wellfounded_Olex__prod(X4,X5,iPr_def_11,iPr_def_12),tc_prod(iPr_def_13,iPr_def_13)) ),
    inference(superposition,[status(thm)],[c_7266,c_814]) ).

tcf(c_145531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(X3,X0,iPr_def_11,iPr_def_12),c_Pair(X3,X1,iPr_def_11,iPr_def_12),iPr_def_13,iPr_def_13),c_Recdef_Osame__fst(X4,X2,iPr_def_11,iPr_def_12),tc_prod(iPr_def_13,iPr_def_13))
      | ~ hBOOL(hAPP(X4,X3))
      | ~ c_in(c_Pair(X0,X1,iPr_def_12,iPr_def_12),hAPP(X2,X3),tc_prod(iPr_def_12,iPr_def_12)) ),
    inference(superposition,[status(thm)],[c_7266,c_810]) ).

tcf(c_145535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X4,X0,X6,X2),c_Pair(X4,X1,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2)),c_Transitive__Closure_Ortrancl(c_Recdef_Osame__fst(X5,X3,X6,X2),tc_prod(X6,X2)),X7)
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_144852]) ).

tcf(c_145536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Recdef_Osame__fst(X5,X3,X6,X2),tc_prod(X6,X2)),c_Pair(c_Pair(X4,X0,X6,X2),c_Pair(X4,X1,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2))))
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_125973]) ).

tcf(c_145537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Recdef_Osame__fst(X5,X3,X6,X2),tc_prod(X6,X2)),c_Pair(c_Pair(X4,X0,X6,X2),c_Pair(X4,X1,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2))))
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_125887]) ).

tcf(c_145538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,X7,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Transitive__Closure_Otrancl(c_Recdef_Osame__fst(X5,X6,X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)))
      | ~ hBOOL(hAPP(X5,X0))
      | ~ c_in(c_Pair(X7,X1,X3,X3),hAPP(X6,X0),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Recdef_Osame__fst(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_810,c_633]) ).

tcf(c_145539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X3),c_Wellfounded_Oacc(c_Recdef_Osame__fst(X4,X5,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3))
      | ~ hBOOL(hAPP(X4,X0))
      | ~ c_in(c_Pair(X6,X1,X3,X3),hAPP(X5,X0),tc_prod(X3,X3))
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Recdef_Osame__fst(X4,X5,X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_810,c_776]) ).

tcf(c_145540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X7,X2),X5,tc_prod(X7,X2))
      | ~ hBOOL(hAPP(X6,X4))
      | ~ c_Relation_Orefl__on(X5,c_Recdef_Osame__fst(X6,X3,X7,X2),tc_prod(X7,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_762]) ).

tcf(c_145541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X0,X7,X2),X5,tc_prod(X7,X2))
      | ~ hBOOL(hAPP(X6,X4))
      | ~ c_Relation_Orefl__on(X5,c_Recdef_Osame__fst(X6,X3,X7,X2),tc_prod(X7,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_761]) ).

tcf(c_145542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(X0,X7,X2,X3) = X4 )
      | ~ hBOOL(hAPP(X5,X0))
      | ~ c_Relation_Osingle__valued(c_Recdef_Osame__fst(X5,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3))
      | ~ c_in(c_Pair(X1,X7,X3,X3),hAPP(X6,X0),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Recdef_Osame__fst(X5,X6,X2,X3),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_810,c_642]) ).

tcf(c_145543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X5,X2),c_Relation_OImage(c_Recdef_Osame__fst(X7,X3,X5,X2),X6,tc_prod(X5,X2),tc_prod(X5,X2)),tc_prod(X5,X2))
      | ~ hBOOL(hAPP(X7,X4))
      | ~ c_in(c_Pair(X4,X0,X5,X2),X6,tc_prod(X5,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_774]) ).

tcf(c_145544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X6,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Recdef_Osame__fst(X5,X3,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2)),tc_prod(X6,X2),tc_prod(X6,X2)),tc_prod(X6,X2))
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_770]) ).

tcf(c_145545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X0,X6,X2),c_Relation_ODomain(c_Recdef_Osame__fst(X5,X3,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2)),tc_prod(X6,X2))
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_768]) ).

tcf(c_145546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(X7,X5,X2,X3),c_Pair(X7,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Pair(c_Pair(X7,X5,X2,X3),c_Pair(X7,X6,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))),X4,tc_prod(tc_prod(tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))))
      | ~ hBOOL(hAPP(X0,X7))
      | ~ c_in(c_Pair(X5,X6,X3,X3),hAPP(X1,X7),tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Recdef_Osame__fst(X0,X1,X2,X3),X4,tc_prod(tc_prod(X2,X3),tc_prod(X2,X3))) ),
    inference(superposition,[status(thm)],[c_810,c_763]) ).

tcf(c_145547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Recdef_Osame__fst(X5,X3,X6,X2),c_Pair(c_Pair(X4,X0,X6,X2),c_Pair(X4,X1,X6,X2),tc_prod(X6,X2),tc_prod(X6,X2))))
      | ~ hBOOL(hAPP(X5,X4))
      | ~ c_in(c_Pair(X0,X1,X2,X2),hAPP(X3,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_810,c_840]) ).

tcf(c_145667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_144819,c_562]) ).

tcf(c_145668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_144819,c_561]) ).

tcf(c_145669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5),X5) ),
    inference(superposition,[status(thm)],[c_144819,c_565]) ).

tcf(c_145670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5),X6),
    inference(superposition,[status(thm)],[c_144819,c_144852]) ).

tcf(c_145671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X3,X2),X4),X5)),
    inference(superposition,[status(thm)],[c_144819,c_125973]) ).

tcf(c_145672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X3,X2),X4),X5)),
    inference(superposition,[status(thm)],[c_144819,c_125887]) ).

tcf(c_145673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X6,X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X6,X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_144819,c_633]) ).

tcf(c_145674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5),X5) ),
    inference(superposition,[status(thm)],[c_144819,c_776]) ).

tcf(c_145675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5) ),
    inference(superposition,[status(thm)],[c_144819,c_762]) ).

tcf(c_145677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X7,X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X7,X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_144819,c_642]) ).

tcf(c_145678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X7,X6),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_144819,c_774]) ).

tcf(c_145679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_144819,c_770]) ).

tcf(c_145680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),X5,X6),X5),
    inference(superposition,[status(thm)],[c_144819,c_768]) ).

tcf(c_145681,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X3,X2),X4,X5) ),
    inference(superposition,[status(thm)],[c_144819,c_763]) ).

tcf(c_145700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X3,X2),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_145677,c_144819]) ).

tcf(c_145703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X6,X5),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_145673,c_144819]) ).

tcf(c_145710,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X5))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),t_a),t_a)
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3)),t_a,t_a),X4,X3) ),
    inference(superposition,[status(thm)],[c_144828,c_560]) ).

tcf(c_145711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X5))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinduct__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3)),t_a,t_a),X4,X3) ),
    inference(superposition,[status(thm)],[c_144828,c_564]) ).

tcf(c_145712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X5))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),t_a),t_a)
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3)),t_a,t_a),X4,X3) ),
    inference(superposition,[status(thm)],[c_144828,c_562]) ).

tcf(c_145713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X5))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X5,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),t_a),t_a)
      | ~ c_in(c_Pair(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3)),t_a,t_a),X4,X3) ),
    inference(superposition,[status(thm)],[c_144828,c_561]) ).

tcf(c_145714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,X6))
      | hBOOL(hAPP(X1,X0))
      | ~ c_in(X6,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),X5),X5)
      | ~ c_in(c_Pair(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X2,X3),X4,X3,X3),X5),X5,X5),X4,X3) ),
    inference(superposition,[status(thm)],[c_144828,c_565]) ).

tcf(c_145715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X1,X2,X2),X4),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_144828,c_144852]) ).

tcf(c_145716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X1,X2,X2),X4),X0))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_144828,c_125973]) ).

tcf(c_145717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X2),X1,X2,X2),X4),X0))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_144828,c_125887]) ).

tcf(c_145718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X4),X5,X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X6,X0,X2,X2),X5,X4)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,X4),X5,X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_144828,c_633]) ).

tcf(c_145719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X4),X4)
      | ~ c_in(c_Pair(X5,X0,X4,X4),X3,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X4),X4) ),
    inference(superposition,[status(thm)],[c_144828,c_776]) ).

tcf(c_145720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | ~ c_in(c_Pair(X5,X6,X4,X4),X3,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X4) ),
    inference(superposition,[status(thm)],[c_144828,c_762]) ).

tcf(c_145721,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,X0,X4)
      | ~ c_in(c_Pair(X5,X6,X4,X4),X3,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X4) ),
    inference(superposition,[status(thm)],[c_144828,c_761]) ).

tcf(c_145722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_in(c_Pair(X0,X7,X2,X3),X6,X5)
      | ~ c_Relation_Osingle__valued(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X4,X5),X6,X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X4,X5),X6,X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_144828,c_642]) ).

tcf(c_145723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Relation_OImage(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X7,X5),X4,X5,X5),X6,X2,X3),X3)
      | ~ c_in(X0,X6,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_144828,c_774]) ).

tcf(c_145724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X6,X5),X4,X5,X5),X2,X3),X3,X2),X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_144828,c_770]) ).

tcf(c_145725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X6,X5),X4,X5,X5),X2,X3),X2)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_144828,c_768]) ).

tcf(c_145726,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_in(X5,X2,X1)
      | ~ c_Relation_Orefl__on(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1,X1),X3,X4) ),
    inference(superposition,[status(thm)],[c_144828,c_763]) ).

tcf(c_145824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X2)
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125836,c_127263]) ).

tcf(c_145846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,X0,X2)
      | c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_125852,c_127263]) ).

tcf(c_145859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126388,c_841]) ).

tcf(c_145860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X3)),X3,X3),X3),
    inference(superposition,[status(thm)],[c_743,c_126457]) ).

tcf(c_145861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,tc_prod(X3,X3),X4)),X5),tc_prod(X3,X3),X4),X3),X6),
    inference(superposition,[status(thm)],[c_126457,c_144852]) ).

tcf(c_145862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,tc_prod(X3,X3),X4)),X5),tc_prod(X3,X3),X4),X3),X1)),
    inference(superposition,[status(thm)],[c_126457,c_125973]) ).

tcf(c_145863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,tc_prod(X3,X3),X4)),X5),tc_prod(X3,X3),X4),X3),X1)),
    inference(superposition,[status(thm)],[c_126457,c_125887]) ).

tcf(c_145864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,tc_prod(X2,X2),X6)),X7),tc_prod(X2,X2),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,tc_prod(X2,X2),X6)),X7),tc_prod(X2,X2),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126457,c_633]) ).

tcf(c_145865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3),X5)),X6),tc_prod(X3,X3),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3),X5)),X6),tc_prod(X3,X3),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_126457,c_776]) ).

tcf(c_145866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4),X6)),X7),tc_prod(X4,X4),X6),X4) ),
    inference(superposition,[status(thm)],[c_126457,c_762]) ).

tcf(c_145867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4),X6)),X7),tc_prod(X4,X4),X6),X4) ),
    inference(superposition,[status(thm)],[c_126457,c_761]) ).

tcf(c_145868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,tc_prod(X2,X3),X7)),X8),tc_prod(X2,X3),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,tc_prod(X2,X3),X7)),X8),tc_prod(X2,X3),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126457,c_642]) ).

tcf(c_145869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,tc_prod(X2,X5),X7)),X8),tc_prod(X2,X5),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126457,c_774]) ).

tcf(c_145870,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4),X6)),X7),tc_prod(X3,X4),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126457,c_770]) ).

tcf(c_145871,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,tc_prod(X3,X4),X6)),X7),tc_prod(X3,X4),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126457,c_768]) ).

tcf(c_145872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X3,X3),X6,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6,X3) ),
    inference(superposition,[status(thm)],[c_126457,c_763]) ).

tcf(c_145873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X1)),
    inference(superposition,[status(thm)],[c_126457,c_840]) ).

tcf(c_145889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,tc_prod(X3,X3),X4)),X5),tc_prod(X3,X3),X4),X3),X6),
    inference(superposition,[status(thm)],[c_126467,c_144852]) ).

tcf(c_145890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,tc_prod(X3,X3),X4)),X5),tc_prod(X3,X3),X4),X3),X1)),
    inference(superposition,[status(thm)],[c_126467,c_125973]) ).

tcf(c_145891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,tc_prod(X3,X3),X4)),X5),tc_prod(X3,X3),X4),X3),X1)),
    inference(superposition,[status(thm)],[c_126467,c_125887]) ).

tcf(c_145892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,tc_prod(X2,X2),X6)),X7),tc_prod(X2,X2),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,tc_prod(X2,X2),X6)),X7),tc_prod(X2,X2),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126467,c_633]) ).

tcf(c_145893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3),X5)),X6),tc_prod(X3,X3),X5),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3),X5)),X6),tc_prod(X3,X3),X5),X3),X3) ),
    inference(superposition,[status(thm)],[c_126467,c_776]) ).

tcf(c_145894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4),X6)),X7),tc_prod(X4,X4),X6),X4) ),
    inference(superposition,[status(thm)],[c_126467,c_762]) ).

tcf(c_145895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4),X6)),X7),tc_prod(X4,X4),X6),X4) ),
    inference(superposition,[status(thm)],[c_126467,c_761]) ).

tcf(c_145896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,tc_prod(X2,X3),X7)),X8),tc_prod(X2,X3),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,tc_prod(X2,X3),X7)),X8),tc_prod(X2,X3),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126467,c_642]) ).

tcf(c_145897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,tc_prod(X2,X5),X7)),X8),tc_prod(X2,X5),X7),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126467,c_774]) ).

tcf(c_145898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4),X6)),X7),tc_prod(X3,X4),X6),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_126467,c_770]) ).

tcf(c_145899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,tc_prod(X3,X4),X6)),X7),tc_prod(X3,X4),X6),X3,X4),X3),
    inference(superposition,[status(thm)],[c_126467,c_768]) ).

tcf(c_145900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X1,X3,X3),X6,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6,X3) ),
    inference(superposition,[status(thm)],[c_126467,c_763]) ).

tcf(c_145901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X1)),
    inference(superposition,[status(thm)],[c_126467,c_840]) ).

tcf(c_145922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126496,c_562]) ).

tcf(c_145923,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126496,c_561]) ).

tcf(c_145924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126496,c_565]) ).

tcf(c_145925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126496,c_144852]) ).

tcf(c_145926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126496,c_125973]) ).

tcf(c_145927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126496,c_125887]) ).

tcf(c_145928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126496,c_633]) ).

tcf(c_145929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126496,c_776]) ).

tcf(c_145930,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126496,c_762]) ).

tcf(c_145932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126496,c_642]) ).

tcf(c_145933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126496,c_774]) ).

tcf(c_145934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126496,c_770]) ).

tcf(c_145935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126496,c_768]) ).

tcf(c_145936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126496,c_763]) ).

tcf(c_145937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126496,c_840]) ).

tcf(c_145955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_145932,c_126496]) ).

tcf(c_145958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_145928,c_126496]) ).

tcf(c_145978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X3,iPr_def_12,iPr_def_12),X5,tc_prod(iPr_def_12,iPr_def_12))
      | c_in(c_Pair(X0,X2,iPr_def_11,iPr_def_11),X4,tc_prod(iPr_def_11,iPr_def_11))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),c_Pair(X2,X3,iPr_def_11,iPr_def_12),iPr_def_13,iPr_def_13),c_Wellfounded_Olex__prod(X4,X5,iPr_def_11,iPr_def_12),tc_prod(iPr_def_13,iPr_def_13)) ),
    inference(superposition,[status(thm)],[c_7266,c_811]) ).

tcf(c_145995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_Pair(X3,X2,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_Relation_Osingle__valued(X0,X1,X1)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_563,c_793]) ).

tcf(c_145996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | c_in(c_Pair(X3,X2,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | c_in(c_Pair(X2,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | ~ c_Relation_Osingle__valued(X0,X1,X1)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Ortrancl(X0,X1),X2,X1),X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
    inference(superposition,[status(thm)],[c_566,c_793]) ).

tcf(c_145997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(X1,X2,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_567,c_793]) ).

tcf(c_145998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X0,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(X1,X2,X2)
      | ~ c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X2)
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X0,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_568,c_793]) ).

tcf(c_145999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,X3,X2),X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_783,c_793]) ).

tcf(c_146000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | c_in(c_Pair(X1,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X2,t_a,t_a)
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,t_a),t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,t_a)),X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_785,c_793]) ).

tcf(c_146001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X3,X2,X2),X2,X2)
      | ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_790,c_793]) ).

tcf(c_146002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X0,X1,X2),X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X2,t_a,t_a)
      | ~ c_in(c_Pair(X0,X3,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a))
      | ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(X2,t_a),tc_prod(t_a,t_a)) ),
    inference(superposition,[status(thm)],[c_792,c_793]) ).

tcf(c_146003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Transitive__Closure_Ortrancl(X3,X2),X0,X1,X2),X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_801,c_793]) ).

tcf(c_146004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3))
      | c_in(c_Pair(X2,X4,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3))
      | ( X1 = X2 )
      | ~ c_Relation_Osingle__valued(X0,X3,X3)
      | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X0,X1,X2,X3),X4,X3,X3),c_Transitive__Closure_Ortrancl(X0,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_802,c_793]) ).

tcf(c_146005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(X2,X3,X3)
      | ~ c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X3),tc_prod(X3,X3))
      | ~ c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X0,X1,c_Transitive__Closure_Ortrancl(X2,X3),X3),X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_803,c_793]) ).

tcf(c_146007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126015,c_793]) ).

tcf(c_146008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126019,c_793]) ).

tcf(c_146009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126024,c_793]) ).

tcf(c_146010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126026,c_793]) ).

tcf(c_146011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126028,c_793]) ).

tcf(c_146012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126079,c_793]) ).

tcf(c_146013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126084,c_793]) ).

tcf(c_146015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126110,c_793]) ).

tcf(c_146016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126112,c_793]) ).

tcf(c_146017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126143,c_793]) ).

tcf(c_146018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126242,c_793]) ).

tcf(c_146019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126149,c_793]) ).

tcf(c_146020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126155,c_793]) ).

tcf(c_146021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126161,c_793]) ).

tcf(c_146023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126249,c_793]) ).

tcf(c_146024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126289,c_793]) ).

tcf(c_146025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126295,c_793]) ).

tcf(c_146026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126397,c_793]) ).

tcf(c_146027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126399,c_793]) ).

tcf(c_146029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126413,c_793]) ).

tcf(c_146030,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130451,c_793]) ).

tcf(c_146031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126717,c_793]) ).

tcf(c_146032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126724,c_793]) ).

tcf(c_146033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126759,c_793]) ).

tcf(c_146034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126766,c_793]) ).

tcf(c_146035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126774,c_793]) ).

tcf(c_146036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126082,c_793]) ).

tcf(c_146037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126781,c_793]) ).

tcf(c_146038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126256,c_793]) ).

tcf(c_146039,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126246,c_793]) ).

tcf(c_146040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126578,c_793]) ).

tcf(c_146041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126659,c_793]) ).

tcf(c_146042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126789,c_793]) ).

tcf(c_146043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126796,c_793]) ).

tcf(c_146044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126837,c_793]) ).

tcf(c_146045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130915,c_793]) ).

tcf(c_146046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130936,c_793]) ).

tcf(c_146047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_128047,c_793]) ).

tcf(c_146048,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130944,c_793]) ).

tcf(c_146049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131331,c_793]) ).

tcf(c_146050,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131357,c_793]) ).

tcf(c_146051,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131383,c_793]) ).

tcf(c_146052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(X0,X4,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_131390,c_793]) ).

tcf(c_146053,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130960,c_793]) ).

tcf(c_146054,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130974,c_793]) ).

tcf(c_146055,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130925,c_793]) ).

tcf(c_146056,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130457,c_793]) ).

tcf(c_146057,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132430,c_793]) ).

tcf(c_146058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132446,c_793]) ).

tcf(c_146059,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132465,c_793]) ).

tcf(c_146060,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132493,c_793]) ).

tcf(c_146061,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X2),X4,X5,X6)),X5,X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X3,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_130912,c_793]) ).

tcf(c_146062,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_132506,c_793]) ).

tcf(c_146063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134102,c_793]) ).

tcf(c_146064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),X3,X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_135103,c_793]) ).

tcf(c_146065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134143,c_793]) ).

tcf(c_146066,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X7,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_134166,c_793]) ).

tcf(c_146067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_626,c_793]) ).

tcf(c_146068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(X3,X2),X2,X2)
      | ~ c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_853,c_793]) ).

tcf(c_146384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X1,X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_573,c_7263,c_7265]) ).

tcf(c_146385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X1,X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X4),
    inference(superposition,[status(thm)],[c_146384,c_144852]) ).

tcf(c_146386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_146384,c_125973]) ).

tcf(c_146387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_146384,c_125887]) ).

tcf(c_146388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X4,iPr_def_10),X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_146384,c_633]) ).

tcf(c_146389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X3,iPr_def_10),X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146384,c_776]) ).

tcf(c_146390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146384,c_762]) ).

tcf(c_146391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146384,c_761]) ).

tcf(c_146392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( c_Pair(X1,X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X3 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_146384,c_642]) ).

tcf(c_146393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146384,c_774]) ).

tcf(c_146394,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_146384,c_770]) ).

tcf(c_146395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_146384,c_768]) ).

tcf(c_146396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_146384,c_763]) ).

tcf(c_146397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_146384,c_840]) ).

tcf(c_146420,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_822,c_7263,c_7265]) ).

tcf(c_146421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X3),
    inference(superposition,[status(thm)],[c_146420,c_144852]) ).

tcf(c_146422,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_146420,c_125973]) ).

tcf(c_146423,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_146420,c_125887]) ).

tcf(c_146424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_146420,c_633]) ).

tcf(c_146425,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146420,c_776]) ).

tcf(c_146426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146420,c_762]) ).

tcf(c_146427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146420,c_761]) ).

tcf(c_146428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X2 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_146420,c_642]) ).

tcf(c_146429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X3),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_146420,c_774]) ).

tcf(c_146430,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_146420,c_770]) ).

tcf(c_146431,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_146420,c_768]) ).

tcf(c_146432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_146420,c_763]) ).

tcf(c_146433,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_146420,c_840]) ).

tcf(c_146500,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X4),X4),
    inference(superposition,[status(thm)],[c_743,c_126497]) ).

tcf(c_146506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126497,c_562]) ).

tcf(c_146507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126497,c_561]) ).

tcf(c_146508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126497,c_565]) ).

tcf(c_146509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126497,c_144852]) ).

tcf(c_146510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126497,c_125973]) ).

tcf(c_146511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126497,c_125887]) ).

tcf(c_146512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126497,c_633]) ).

tcf(c_146513,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126497,c_776]) ).

tcf(c_146514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126497,c_762]) ).

tcf(c_146516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126497,c_642]) ).

tcf(c_146517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126497,c_774]) ).

tcf(c_146518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126497,c_770]) ).

tcf(c_146519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126497,c_768]) ).

tcf(c_146520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126497,c_763]) ).

tcf(c_146521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126497,c_840]) ).

tcf(c_146539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_146516,c_126497]) ).

tcf(c_146542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_146512,c_126497]) ).

tcf(c_146584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126498,c_562]) ).

tcf(c_146585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126498,c_561]) ).

tcf(c_146586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126498,c_565]) ).

tcf(c_146587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126498,c_144852]) ).

tcf(c_146588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126498,c_125973]) ).

tcf(c_146589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126498,c_125887]) ).

tcf(c_146590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126498,c_633]) ).

tcf(c_146591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126498,c_776]) ).

tcf(c_146592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126498,c_762]) ).

tcf(c_146594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126498,c_642]) ).

tcf(c_146595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126498,c_774]) ).

tcf(c_146596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126498,c_770]) ).

tcf(c_146597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126498,c_768]) ).

tcf(c_146598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126498,c_763]) ).

tcf(c_146599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126498,c_840]) ).

tcf(c_146617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_146594,c_126498]) ).

tcf(c_146620,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_146590,c_126498]) ).

tcf(c_146646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X4),X4),
    inference(superposition,[status(thm)],[c_743,c_126499]) ).

tcf(c_146651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126499,c_562]) ).

tcf(c_146652,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126499,c_561]) ).

tcf(c_146653,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126499,c_565]) ).

tcf(c_146654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126499,c_144852]) ).

tcf(c_146655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126499,c_125973]) ).

tcf(c_146656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126499,c_125887]) ).

tcf(c_146657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126499,c_633]) ).

tcf(c_146658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126499,c_776]) ).

tcf(c_146659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126499,c_762]) ).

tcf(c_146661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126499,c_642]) ).

tcf(c_146662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126499,c_774]) ).

tcf(c_146663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126499,c_770]) ).

tcf(c_146664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126499,c_768]) ).

tcf(c_146665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126499,c_763]) ).

tcf(c_146666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126499,c_840]) ).

tcf(c_146684,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_146661,c_126499]) ).

tcf(c_146687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_146657,c_126499]) ).

tcf(c_146739,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125697,c_126501]) ).

tcf(c_146740,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125698,c_126501]) ).

tcf(c_146741,plain,
    ! [X0: $i,X1: $i] : c_in(X0,c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125699,c_126501]) ).

tcf(c_146742,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125928,c_126501]) ).

tcf(c_146743,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125931,c_126501]) ).

tcf(c_146744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125935,c_126501]) ).

tcf(c_146745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125797,c_126501]) ).

tcf(c_146746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125747,c_126501]) ).

tcf(c_146747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125796,c_126501]) ).

tcf(c_146748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125799,c_126501]) ).

tcf(c_146749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125939,c_126501]) ).

tcf(c_146750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126382,c_126501]) ).

tcf(c_146751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126383,c_126501]) ).

tcf(c_146752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130441,c_126501]) ).

tcf(c_146753,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126015,c_126501]) ).

tcf(c_146754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126019,c_126501]) ).

tcf(c_146755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126024,c_126501]) ).

tcf(c_146756,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126026,c_126501]) ).

tcf(c_146757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126028,c_126501]) ).

tcf(c_146758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126030,c_126501]) ).

tcf(c_146759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126079,c_126501]) ).

tcf(c_146760,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126084,c_126501]) ).

tcf(c_146761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126086,c_126501]) ).

tcf(c_146762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126110,c_126501]) ).

tcf(c_146763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126112,c_126501]) ).

tcf(c_146764,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126143,c_126501]) ).

tcf(c_146765,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126146,c_126501]) ).

tcf(c_146766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126242,c_126501]) ).

tcf(c_146767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126149,c_126501]) ).

tcf(c_146768,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126152,c_126501]) ).

tcf(c_146769,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126155,c_126501]) ).

tcf(c_146770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126158,c_126501]) ).

tcf(c_146771,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126161,c_126501]) ).

tcf(c_146772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126163,c_126501]) ).

tcf(c_146773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126249,c_126501]) ).

tcf(c_146774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126252,c_126501]) ).

tcf(c_146775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126289,c_126501]) ).

tcf(c_146776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126292,c_126501]) ).

tcf(c_146777,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126295,c_126501]) ).

tcf(c_146778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126297,c_126501]) ).

tcf(c_146779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126397,c_126501]) ).

tcf(c_146780,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126399,c_126501]) ).

tcf(c_146781,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126413,c_126501]) ).

tcf(c_146782,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130451,c_126501]) ).

tcf(c_146783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126714,c_126501]) ).

tcf(c_146784,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126717,c_126501]) ).

tcf(c_146785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126720,c_126501]) ).

tcf(c_146786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126724,c_126501]) ).

tcf(c_146787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126755,c_126501]) ).

tcf(c_146788,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126759,c_126501]) ).

tcf(c_146789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,iPr_def_11,iPr_def_12)),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126762,c_126501]) ).

tcf(c_146790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126766,c_126501]) ).

tcf(c_146791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126770,c_126501]) ).

tcf(c_146792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126774,c_126501]) ).

tcf(c_146793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126777,c_126501]) ).

tcf(c_146794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,iPr_def_11,iPr_def_12),X3,iPr_def_13,X4)),X5),iPr_def_13,X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126457,c_126501]) ).

tcf(c_146795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,iPr_def_11,iPr_def_12),X3,iPr_def_13,X4)),X5),iPr_def_13,X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126467,c_126501]) ).

tcf(c_146796,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125711,c_126501]) ).

tcf(c_146797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126082,c_126501]) ).

tcf(c_146798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125746,c_126501]) ).

tcf(c_146799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126528,c_126501]) ).

tcf(c_146800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126533,c_126501]) ).

tcf(c_146801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126781,c_126501]) ).

tcf(c_146802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126558,c_126501]) ).

tcf(c_146803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126256,c_126501]) ).

tcf(c_146804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126286,c_126501]) ).

tcf(c_146805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126246,c_126501]) ).

tcf(c_146806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125942,c_126501]) ).

tcf(c_146807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126578,c_126501]) ).

tcf(c_146808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126785,c_126501]) ).

tcf(c_146809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126584,c_126501]) ).

tcf(c_146810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126659,c_126501]) ).

tcf(c_146811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126665,c_126501]) ).

tcf(c_146812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,X3,X4)),X3,X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_125830,c_126501]) ).

tcf(c_146813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126672,c_126501]) ).

tcf(c_146814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126871,c_126501]) ).

tcf(c_146815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126496,c_126501]) ).

tcf(c_146816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126497,c_126501]) ).

tcf(c_146817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126498,c_126501]) ).

tcf(c_146818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126499,c_126501]) ).

tcf(c_146819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126789,c_126501]) ).

tcf(c_146820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126792,c_126501]) ).

tcf(c_146821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126796,c_126501]) ).

tcf(c_146822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126834,c_126501]) ).

tcf(c_146823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126837,c_126501]) ).

tcf(c_146824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,iPr_def_11,iPr_def_12)),X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126839,c_126501]) ).

tcf(c_146825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130915,c_126501]) ).

tcf(c_146826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127183,c_126501]) ).

tcf(c_146827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127225,c_126501]) ).

tcf(c_146828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130918,c_126501]) ).

tcf(c_146829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130936,c_126501]) ).

tcf(c_146830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_128047,c_126501]) ).

tcf(c_146831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_128082,c_126501]) ).

tcf(c_146832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130940,c_126501]) ).

tcf(c_146833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,iPr_def_11,iPr_def_12),X3,X4,X5)),X4,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129469,c_126501]) ).

tcf(c_146834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129474,c_126501]) ).

tcf(c_146835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129480,c_126501]) ).

tcf(c_146836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129487,c_126501]) ).

tcf(c_146837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129493,c_126501]) ).

tcf(c_146838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130944,c_126501]) ).

tcf(c_146839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129942,c_126501]) ).

tcf(c_146840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_129951,c_126501]) ).

tcf(c_146841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130947,c_126501]) ).

tcf(c_146842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(X2,X3),X3),iPr_def_11,iPr_def_12),iPr_def_11)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,tc_prod(X3,X3)) ),
    inference(superposition,[status(thm)],[c_130430,c_126501]) ).

tcf(c_146843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131331,c_126501]) ).

tcf(c_146844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131335,c_126501]) ).

tcf(c_146845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131357,c_126501]) ).

tcf(c_146846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131379,c_126501]) ).

tcf(c_146847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131383,c_126501]) ).

tcf(c_146848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131387,c_126501]) ).

tcf(c_146849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131390,c_126501]) ).

tcf(c_146850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,iPr_def_11,iPr_def_12)),X3),X4),X5),X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131392,c_126501]) ).

tcf(c_146851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130960,c_126501]) ).

tcf(c_146852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130967,c_126501]) ).

tcf(c_146853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130974,c_126501]) ).

tcf(c_146854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_131327,c_126501]) ).

tcf(c_146855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130925,c_126501]) ).

tcf(c_146856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130932,c_126501]) ).

tcf(c_146857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130457,c_126501]) ).

tcf(c_146858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130446,c_126501]) ).

tcf(c_146859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132430,c_126501]) ).

tcf(c_146860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132438,c_126501]) ).

tcf(c_146861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132446,c_126501]) ).

tcf(c_146862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132453,c_126501]) ).

tcf(c_146863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132465,c_126501]) ).

tcf(c_146864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132486,c_126501]) ).

tcf(c_146865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132493,c_126501]) ).

tcf(c_146866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132499,c_126501]) ).

tcf(c_146867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,X3,X4)),X3,X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_130912,c_126501]) ).

tcf(c_146868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,X3,X4)),X3,X4),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126585,c_126501]) ).

tcf(c_146869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_132506,c_126501]) ).

tcf(c_146870,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134095,c_126501]) ).

tcf(c_146871,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134102,c_126501]) ).

tcf(c_146872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134109,c_126501]) ).

tcf(c_146873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X3,iPr_def_11,iPr_def_12),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_134992,c_126501]) ).

tcf(c_146874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,iPr_def_11,iPr_def_12),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_135103,c_126501]) ).

tcf(c_146875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,iPr_def_11,iPr_def_12),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_135118,c_126501]) ).

tcf(c_146876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134143,c_126501]) ).

tcf(c_146877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134150,c_126501]) ).

tcf(c_146878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134166,c_126501]) ).

tcf(c_146879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_134850,c_126501]) ).

tcf(c_146880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(c_Pair(X0,X3,iPr_def_11,iPr_def_12),X4,X5,X6)),X5,X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_97184,c_126501]) ).

tcf(c_146881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,X3,X4)),X5),X3,X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_97186,c_126501]) ).

tcf(c_146882,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,X3,X4)),X5),X3,X4),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_97187,c_126501]) ).

tcf(c_146883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5,X6),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_97192,c_126501]) ).

tcf(c_146884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X4,X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_144819,c_126501]) ).

tcf(c_146885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_OImage(c_Transitive__Closure_Ortrancl(X4,X3),X2,X3,X3),iPr_def_11,iPr_def_12),iPr_def_11)
      | ~ c_in(c_Pair(X0,X1,iPr_def_11,iPr_def_12),X2,X3) ),
    inference(superposition,[status(thm)],[c_144828,c_126501]) ).

tcf(c_147138,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X1) ),
    inference(superposition,[status(thm)],[c_743,c_126613]) ).

tcf(c_147139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,tc_prod(X2,X2)),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_126613,c_144852]) ).

tcf(c_147140,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,tc_prod(X1,X1)))) ),
    inference(superposition,[status(thm)],[c_126613,c_125973]) ).

tcf(c_147141,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,tc_prod(X1,X1)))) ),
    inference(superposition,[status(thm)],[c_126613,c_125887]) ).

tcf(c_147142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X1),X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(X0,X1,X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_126613,c_763]) ).

tcf(c_147143,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X2,X1))) ),
    inference(superposition,[status(thm)],[c_126613,c_840]) ).

tcf(c_147178,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X1) ),
    inference(superposition,[status(thm)],[c_743,c_126635]) ).

tcf(c_147179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,tc_prod(X2,X2)),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,tc_prod(X2,X2),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_126635,c_144852]) ).

tcf(c_147180,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,tc_prod(X1,X1)))) ),
    inference(superposition,[status(thm)],[c_126635,c_125973]) ).

tcf(c_147181,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,tc_prod(X1,X1)))) ),
    inference(superposition,[status(thm)],[c_126635,c_125887]) ).

tcf(c_147182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X1),X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(X0,X1,X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_126635,c_763]) ).

tcf(c_147183,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X2,X1))) ),
    inference(superposition,[status(thm)],[c_126635,c_840]) ).

tcf(c_147203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126679,c_562]) ).

tcf(c_147204,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126679,c_561]) ).

tcf(c_147205,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126679,c_565]) ).

tcf(c_147206,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126679,c_144852]) ).

tcf(c_147207,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126679,c_125973]) ).

tcf(c_147208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126679,c_125887]) ).

tcf(c_147209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126679,c_633]) ).

tcf(c_147210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126679,c_776]) ).

tcf(c_147211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126679,c_762]) ).

tcf(c_147213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126679,c_642]) ).

tcf(c_147214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126679,c_774]) ).

tcf(c_147215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126679,c_770]) ).

tcf(c_147216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126679,c_768]) ).

tcf(c_147217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126679,c_763]) ).

tcf(c_147218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126679,c_840]) ).

tcf(c_147219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126679,c_126501]) ).

tcf(c_147237,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_147213,c_126679]) ).

tcf(c_147240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_147209,c_126679]) ).

tcf(c_147271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X4),X4),
    inference(superposition,[status(thm)],[c_743,c_126687]) ).

tcf(c_147278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126687,c_562]) ).

tcf(c_147279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126687,c_561]) ).

tcf(c_147280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126687,c_565]) ).

tcf(c_147281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126687,c_144852]) ).

tcf(c_147282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126687,c_125973]) ).

tcf(c_147283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126687,c_125887]) ).

tcf(c_147284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126687,c_633]) ).

tcf(c_147285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126687,c_776]) ).

tcf(c_147286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126687,c_762]) ).

tcf(c_147288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126687,c_642]) ).

tcf(c_147289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126687,c_774]) ).

tcf(c_147290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126687,c_770]) ).

tcf(c_147291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126687,c_768]) ).

tcf(c_147292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126687,c_763]) ).

tcf(c_147293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126687,c_840]) ).

tcf(c_147294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126687,c_126501]) ).

tcf(c_147312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_147288,c_126687]) ).

tcf(c_147315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_147284,c_126687]) ).

tcf(c_147377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126694,c_562]) ).

tcf(c_147378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126694,c_561]) ).

tcf(c_147379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126694,c_565]) ).

tcf(c_147380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126694,c_144852]) ).

tcf(c_147381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126694,c_125973]) ).

tcf(c_147382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126694,c_125887]) ).

tcf(c_147383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126694,c_633]) ).

tcf(c_147384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126694,c_776]) ).

tcf(c_147385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126694,c_762]) ).

tcf(c_147387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126694,c_642]) ).

tcf(c_147388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126694,c_774]) ).

tcf(c_147389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126694,c_770]) ).

tcf(c_147390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126694,c_768]) ).

tcf(c_147391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126694,c_763]) ).

tcf(c_147392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126694,c_840]) ).

tcf(c_147393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126694,c_126501]) ).

tcf(c_147411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_147387,c_126694]) ).

tcf(c_147414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_147383,c_126694]) ).

tcf(c_147431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X4),X4),
    inference(superposition,[status(thm)],[c_743,c_126701]) ).

tcf(c_147437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126701,c_562]) ).

tcf(c_147438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126701,c_561]) ).

tcf(c_147439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126701,c_565]) ).

tcf(c_147440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126701,c_144852]) ).

tcf(c_147441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126701,c_125973]) ).

tcf(c_147442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126701,c_125887]) ).

tcf(c_147443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126701,c_633]) ).

tcf(c_147444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126701,c_776]) ).

tcf(c_147445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126701,c_762]) ).

tcf(c_147447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126701,c_642]) ).

tcf(c_147448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126701,c_774]) ).

tcf(c_147449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126701,c_770]) ).

tcf(c_147450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126701,c_768]) ).

tcf(c_147451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126701,c_763]) ).

tcf(c_147452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126701,c_840]) ).

tcf(c_147453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126701,c_126501]) ).

tcf(c_147471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_147447,c_126701]) ).

tcf(c_147474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_147443,c_126701]) ).

tcf(c_147560,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_557,c_7263,c_7265]) ).

tcf(c_147561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X3),
    inference(superposition,[status(thm)],[c_147560,c_144852]) ).

tcf(c_147562,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X1,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147560,c_125973]) ).

tcf(c_147563,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X1,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147560,c_125887]) ).

tcf(c_147564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X3,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X0,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X1,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X0,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X1,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X2),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147560,c_633]) ).

tcf(c_147565,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X0,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X0,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147560,c_776]) ).

tcf(c_147566,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147560,c_762]) ).

tcf(c_147567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147560,c_761]) ).

tcf(c_147568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X2 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147560,c_642]) ).

tcf(c_147569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X3),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147560,c_774]) ).

tcf(c_147570,plain,
    ! [X0: $i,X1: $i] : c_in(c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X0,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147560,c_770]) ).

tcf(c_147571,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147560,c_768]) ).

tcf(c_147572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147560,c_763]) ).

tcf(c_147573,plain,
    ! [X0: $i,X1: $i,X2: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OCast(X1,c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147560,c_840]) ).

tcf(c_147589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_646,c_7263,c_7265]) ).

tcf(c_147590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X4),
    inference(superposition,[status(thm)],[c_147589,c_144852]) ).

tcf(c_147591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147589,c_125973]) ).

tcf(c_147592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147589,c_125887]) ).

tcf(c_147593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147589,c_633]) ).

tcf(c_147594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147589,c_776]) ).

tcf(c_147596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147589,c_761]) ).

tcf(c_147597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X3 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147589,c_642]) ).

tcf(c_147598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147589,c_774]) ).

tcf(c_147600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147589,c_768]) ).

tcf(c_147601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147589,c_763]) ).

tcf(c_147602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147589,c_840]) ).

tcf(c_147616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_647,c_7263,c_7265]) ).

tcf(c_147617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X4),
    inference(superposition,[status(thm)],[c_147616,c_144852]) ).

tcf(c_147618,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147616,c_125973]) ).

tcf(c_147619,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147616,c_125887]) ).

tcf(c_147620,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X4,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147616,c_633]) ).

tcf(c_147621,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X3,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147616,c_776]) ).

tcf(c_147623,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147616,c_761]) ).

tcf(c_147624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X3 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147616,c_642]) ).

tcf(c_147625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147616,c_774]) ).

tcf(c_147627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Expr_Oexp_OCast(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147616,c_768]) ).

tcf(c_147628,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147616,c_763]) ).

tcf(c_147629,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OCast(X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147616,c_840]) ).

tcf(c_147660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_650,c_7263,c_7265]) ).

tcf(c_147661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X4),
    inference(superposition,[status(thm)],[c_147660,c_144852]) ).

tcf(c_147662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147660,c_125973]) ).

tcf(c_147663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147660,c_125887]) ).

tcf(c_147664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X4,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147660,c_633]) ).

tcf(c_147665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X3,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147660,c_776]) ).

tcf(c_147667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147660,c_761]) ).

tcf(c_147668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X3 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147660,c_642]) ).

tcf(c_147669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147660,c_774]) ).

tcf(c_147671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_Othrow(X1,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147660,c_768]) ).

tcf(c_147672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147660,c_763]) ).

tcf(c_147673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147660,c_840]) ).

tcf(c_147749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126709,c_562]) ).

tcf(c_147750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126709,c_561]) ).

tcf(c_147751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126709,c_565]) ).

tcf(c_147752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126709,c_144852]) ).

tcf(c_147753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126709,c_125973]) ).

tcf(c_147754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126709,c_125887]) ).

tcf(c_147755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126709,c_633]) ).

tcf(c_147756,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126709,c_776]) ).

tcf(c_147757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126709,c_762]) ).

tcf(c_147759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126709,c_642]) ).

tcf(c_147760,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126709,c_774]) ).

tcf(c_147761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126709,c_770]) ).

tcf(c_147762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126709,c_768]) ).

tcf(c_147763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126709,c_763]) ).

tcf(c_147764,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126709,c_840]) ).

tcf(c_147765,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126709,c_126501]) ).

tcf(c_147783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_147759,c_126709]) ).

tcf(c_147786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_147755,c_126709]) ).

tcf(c_147806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126842,c_841]) ).

tcf(c_147809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126846,c_841]) ).

tcf(c_147821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126854,c_841]) ).

tcf(c_147828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126878,c_562]) ).

tcf(c_147829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_126878,c_561]) ).

tcf(c_147830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126878,c_565]) ).

tcf(c_147831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_126878,c_144852]) ).

tcf(c_147832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126878,c_125973]) ).

tcf(c_147833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_126878,c_125887]) ).

tcf(c_147834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_126878,c_633]) ).

tcf(c_147835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_126878,c_776]) ).

tcf(c_147836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_126878,c_762]) ).

tcf(c_147838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_126878,c_642]) ).

tcf(c_147839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_126878,c_774]) ).

tcf(c_147840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_126878,c_770]) ).

tcf(c_147841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_126878,c_768]) ).

tcf(c_147842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_126878,c_763]) ).

tcf(c_147843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_126878,c_840]) ).

tcf(c_147844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_126878,c_126501]) ).

tcf(c_147862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_147838,c_126878]) ).

tcf(c_147865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_147834,c_126878]) ).

tcf(c_147937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_126883,c_841]) ).

tcf(c_147943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126888,c_841]) ).

tcf(c_147944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_498,c_7263,c_7265]) ).

tcf(c_147945,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_147944,c_144852]) ).

tcf(c_147946,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147944,c_125973]) ).

tcf(c_147947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147944,c_125887]) ).

tcf(c_147948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X4,X5,c_Expr_Oexp_OVal(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147944,c_633]) ).

tcf(c_147949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X3,X4,c_Expr_Oexp_OVal(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147944,c_776]) ).

tcf(c_147950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147944,c_762]) ).

tcf(c_147951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147944,c_761]) ).

tcf(c_147952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147944,c_642]) ).

tcf(c_147953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147944,c_774]) ).

tcf(c_147954,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147944,c_770]) ).

tcf(c_147955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147944,c_768]) ).

tcf(c_147956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147944,c_763]) ).

tcf(c_147957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147944,c_840]) ).

tcf(c_147996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_643,c_7263,c_7265]) ).

tcf(c_147997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_147996,c_144852]) ).

tcf(c_147998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147996,c_125973]) ).

tcf(c_147999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147996,c_125887]) ).

tcf(c_148000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147996,c_633]) ).

tcf(c_148001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,X4,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147996,c_776]) ).

tcf(c_148003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147996,c_761]) ).

tcf(c_148004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147996,c_642]) ).

tcf(c_148005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_147996,c_774]) ).

tcf(c_148007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_147996,c_768]) ).

tcf(c_148008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_147996,c_763]) ).

tcf(c_148009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OCond(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_147996,c_840]) ).

tcf(c_148096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_644,c_7263,c_7265]) ).

tcf(c_148097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_148096,c_144852]) ).

tcf(c_148098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148096,c_125973]) ).

tcf(c_148099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148096,c_125887]) ).

tcf(c_148100,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148096,c_633]) ).

tcf(c_148101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,X4,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148096,c_776]) ).

tcf(c_148103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148096,c_761]) ).

tcf(c_148104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148096,c_642]) ).

tcf(c_148105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148096,c_774]) ).

tcf(c_148107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_148096,c_768]) ).

tcf(c_148108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148096,c_763]) ).

tcf(c_148109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148096,c_840]) ).

tcf(c_148152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_648,c_7263,c_7265]) ).

tcf(c_148153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_148152,c_144852]) ).

tcf(c_148154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148152,c_125973]) ).

tcf(c_148155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148152,c_125887]) ).

tcf(c_148156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148152,c_633]) ).

tcf(c_148157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,X4,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148152,c_776]) ).

tcf(c_148159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148152,c_761]) ).

tcf(c_148160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148152,c_642]) ).

tcf(c_148161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148152,c_774]) ).

tcf(c_148163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_148152,c_768]) ).

tcf(c_148164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148152,c_763]) ).

tcf(c_148165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148152,c_840]) ).

tcf(c_148190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_126896,c_841]) ).

tcf(c_148235,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127191,c_562]) ).

tcf(c_148236,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127191,c_561]) ).

tcf(c_148237,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_127191,c_565]) ).

tcf(c_148238,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_127191,c_144852]) ).

tcf(c_148239,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_127191,c_125973]) ).

tcf(c_148240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_127191,c_125887]) ).

tcf(c_148241,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127191,c_633]) ).

tcf(c_148242,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_127191,c_776]) ).

tcf(c_148243,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_127191,c_762]) ).

tcf(c_148245,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127191,c_642]) ).

tcf(c_148246,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127191,c_774]) ).

tcf(c_148247,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_127191,c_770]) ).

tcf(c_148248,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_127191,c_768]) ).

tcf(c_148249,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_127191,c_763]) ).

tcf(c_148250,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_127191,c_840]) ).

tcf(c_148251,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127191,c_126501]) ).

tcf(c_148269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_148245,c_127191]) ).

tcf(c_148272,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_148241,c_127191]) ).

tcf(c_148283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_127200,c_841]) ).

tcf(c_148308,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127234,c_562]) ).

tcf(c_148309,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(t_a,t_a),X5),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127234,c_561]) ).

tcf(c_148310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_127234,c_565]) ).

tcf(c_148311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X7),
    inference(superposition,[status(thm)],[c_127234,c_144852]) ).

tcf(c_148312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_127234,c_125973]) ).

tcf(c_148313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X4),X5),X4),X6)),
    inference(superposition,[status(thm)],[c_127234,c_125887]) ).

tcf(c_148314,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127234,c_633]) ).

tcf(c_148315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5),X5) ),
    inference(superposition,[status(thm)],[c_127234,c_776]) ).

tcf(c_148316,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X5),X6),X5) ),
    inference(superposition,[status(thm)],[c_127234,c_762]) ).

tcf(c_148318,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X3),X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127234,c_642]) ).

tcf(c_148319,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),tc_prod(X2,X8),X9),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127234,c_774]) ).

tcf(c_148320,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_127234,c_770]) ).

tcf(c_148321,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),tc_prod(X5,X6),X7),X5,X6),X5),
    inference(superposition,[status(thm)],[c_127234,c_768]) ).

tcf(c_148322,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X4,X4),X6,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X4) ),
    inference(superposition,[status(thm)],[c_127234,c_763]) ).

tcf(c_148323,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6)),
    inference(superposition,[status(thm)],[c_127234,c_840]) ).

tcf(c_148324,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),iPr_def_13,X5),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127234,c_126501]) ).

tcf(c_148342,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),tc_prod(X4,X5),X6),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_148318,c_127234]) ).

tcf(c_148345,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),tc_prod(X2,X2),X7),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_148314,c_127234]) ).

tcf(c_148405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_651,c_7263,c_7265]) ).

tcf(c_148406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_148405,c_144852]) ).

tcf(c_148407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148405,c_125973]) ).

tcf(c_148408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148405,c_125887]) ).

tcf(c_148409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148405,c_633]) ).

tcf(c_148410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,X4,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148405,c_776]) ).

tcf(c_148412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148405,c_761]) ).

tcf(c_148413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148405,c_642]) ).

tcf(c_148414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148405,c_774]) ).

tcf(c_148416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_148405,c_768]) ).

tcf(c_148417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148405,c_763]) ).

tcf(c_148418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OCall(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148405,c_840]) ).

tcf(c_148467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_574,c_7263,c_7265]) ).

tcf(c_148468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6),
    inference(superposition,[status(thm)],[c_148467,c_144852]) ).

tcf(c_148469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X1,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148467,c_125973]) ).

tcf(c_148470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X1,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148467,c_125887]) ).

tcf(c_148471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X4,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148467,c_633]) ).

tcf(c_148472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X3,X4,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148467,c_776]) ).

tcf(c_148474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,X4,X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148467,c_761]) ).

tcf(c_148475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X5 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148467,c_642]) ).

tcf(c_148476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X6),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148467,c_774]) ).

tcf(c_148478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_148467,c_768]) ).

tcf(c_148479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,X4,X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,X4,X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148467,c_763]) ).

tcf(c_148480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X1,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148467,c_840]) ).

tcf(c_148515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_649,c_7263,c_7265]) ).

tcf(c_148516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6),
    inference(superposition,[status(thm)],[c_148515,c_144852]) ).

tcf(c_148517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148515,c_125973]) ).

tcf(c_148518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148515,c_125887]) ).

tcf(c_148519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148515,c_633]) ).

tcf(c_148520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X3,X4,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148515,c_776]) ).

tcf(c_148522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148515,c_761]) ).

tcf(c_148523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X5 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148515,c_642]) ).

tcf(c_148524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X6),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148515,c_774]) ).

tcf(c_148526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_148515,c_768]) ).

tcf(c_148527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,X4,X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148515,c_763]) ).

tcf(c_148528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_Othrow(X1,iPr_def_10),X2,X3,X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X1,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148515,c_840]) ).

tcf(c_148577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_578,c_7263,c_7265]) ).

tcf(c_148578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_148577,c_144852]) ).

tcf(c_148579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148577,c_125973]) ).

tcf(c_148580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148577,c_125887]) ).

tcf(c_148581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148577,c_633]) ).

tcf(c_148582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148577,c_776]) ).

tcf(c_148584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,c_Expr_Oexp_Othrow(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148577,c_761]) ).

tcf(c_148585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148577,c_642]) ).

tcf(c_148586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_148577,c_774]) ).

tcf(c_148588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,c_Expr_Oexp_Othrow(X2,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_148577,c_768]) ).

tcf(c_148589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,c_Expr_Oexp_Othrow(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,c_Expr_Oexp_Othrow(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_148577,c_763]) ).

tcf(c_148590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_148577,c_840]) ).

tcf(c_148651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_127242,c_841]) ).

tcf(c_148660,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_127786]) ).

tcf(c_148661,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,X2,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_670,c_127786]) ).

tcf(c_148662,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_684,c_127786]) ).

tcf(c_148663,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X1,X2),X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_127786]) ).

tcf(c_148664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127786,c_560]) ).

tcf(c_148665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127786,c_564]) ).

tcf(c_148666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127786,c_562]) ).

tcf(c_148667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a),c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127786,c_561]) ).

tcf(c_148668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2,X2),c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127786,c_565]) ).

tcf(c_148669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_127786,c_144852]) ).

tcf(c_148670,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_127786,c_125973]) ).

tcf(c_148671,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_127786,c_125887]) ).

tcf(c_148672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127786,c_633]) ).

tcf(c_148673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X3,X0,X2,X2),c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127786,c_776]) ).

tcf(c_148674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127786,c_762]) ).

tcf(c_148675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127786,c_761]) ).

tcf(c_148676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X3),c_Wellfounded_Oacc(X4,tc_prod(X2,X3)),tc_prod(X2,X3))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127786,c_642]) ).

tcf(c_148677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X5),c_Wellfounded_Oacc(X4,tc_prod(X2,X5)),tc_prod(X2,X5))
      | c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(X4,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127786,c_774]) ).

tcf(c_148678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X2,X3),c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_127786,c_770]) ).

tcf(c_148679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X3),c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_127786,c_768]) ).

tcf(c_148680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_127786,c_763]) ).

tcf(c_148681,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2)) ),
    inference(superposition,[status(thm)],[c_127786,c_840]) ).

tcf(c_148682,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,X2,iPr_def_11,iPr_def_12),c_Wellfounded_Oacc(X1,iPr_def_13),iPr_def_13)
      | c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(X1,iPr_def_13,iPr_def_13),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_127786,c_126501]) ).

tcf(c_148821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,X0,X2,tc_prod(X3,X3))),X2,tc_prod(X3,X3)),tc_prod(X3,X3),X2),X3),X4),
    inference(superposition,[status(thm)],[c_127793,c_144852]) ).

tcf(c_148822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,tc_prod(X3,X3))),X2,tc_prod(X3,X3)),tc_prod(X3,X3),X2),X3),X1)),
    inference(superposition,[status(thm)],[c_127793,c_125973]) ).

tcf(c_148823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,tc_prod(X3,X3))),X2,tc_prod(X3,X3)),tc_prod(X3,X3),X2),X3),X1)),
    inference(superposition,[status(thm)],[c_127793,c_125887]) ).

tcf(c_148824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X3,c_Pair(X4,X0,X2,X2),X5,tc_prod(X2,X2))),X5,tc_prod(X2,X2)),tc_prod(X2,X2),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X3,c_Pair(X4,X0,X2,X2),X5,tc_prod(X2,X2))),X5,tc_prod(X2,X2)),tc_prod(X2,X2),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127793,c_633]) ).

tcf(c_148825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3))),X4,tc_prod(X3,X3)),tc_prod(X3,X3),X4),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X0,X3,X3),X4,tc_prod(X3,X3))),X4,tc_prod(X3,X3)),tc_prod(X3,X3),X4),X3),X3) ),
    inference(superposition,[status(thm)],[c_127793,c_776]) ).

tcf(c_148826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))),X5,tc_prod(X4,X4)),tc_prod(X4,X4),X5),X4) ),
    inference(superposition,[status(thm)],[c_127793,c_762]) ).

tcf(c_148827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))),X5,tc_prod(X4,X4)),tc_prod(X4,X4),X5),X4) ),
    inference(superposition,[status(thm)],[c_127793,c_761]) ).

tcf(c_148828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X4,c_Pair(X0,X5,X2,X3),X6,tc_prod(X2,X3))),X6,tc_prod(X2,X3)),tc_prod(X2,X3),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X4,c_Pair(X0,X5,X2,X3),X6,tc_prod(X2,X3))),X6,tc_prod(X2,X3)),tc_prod(X2,X3),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127793,c_642]) ).

tcf(c_148829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X4,c_Pair(X0,X3,X2,X5),X6,tc_prod(X2,X5))),X6,tc_prod(X2,X5)),tc_prod(X2,X5),X6),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127793,c_774]) ).

tcf(c_148830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X0,X3,X4),X5,tc_prod(X3,X4))),X5,tc_prod(X3,X4)),tc_prod(X3,X4),X5),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_127793,c_770]) ).

tcf(c_148831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X0,X2,X3,X4),X5,tc_prod(X3,X4))),X5,tc_prod(X3,X4)),tc_prod(X3,X4),X5),X3,X4),X3),
    inference(superposition,[status(thm)],[c_127793,c_768]) ).

tcf(c_148832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X1,X3,X3),X4,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X3,X2),X4,X3) ),
    inference(superposition,[status(thm)],[c_127793,c_763]) ).

tcf(c_148833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X3,X2),X1)),
    inference(superposition,[status(thm)],[c_127793,c_840]) ).

tcf(c_148834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X0,X2,iPr_def_11,iPr_def_12),X3,iPr_def_13)),X3,iPr_def_13),iPr_def_13,X3),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127793,c_126501]) ).

tcf(c_148867,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_687,c_127804]) ).

tcf(c_148873,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127804,c_562]) ).

tcf(c_148874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127804,c_561]) ).

tcf(c_148875,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127804,c_565]) ).

tcf(c_148876,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X5),
    inference(superposition,[status(thm)],[c_127804,c_144852]) ).

tcf(c_148877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127804,c_125973]) ).

tcf(c_148878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127804,c_125887]) ).

tcf(c_148879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127804,c_633]) ).

tcf(c_148880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127804,c_776]) ).

tcf(c_148881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127804,c_762]) ).

tcf(c_148883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127804,c_642]) ).

tcf(c_148884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127804,c_774]) ).

tcf(c_148885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_127804,c_770]) ).

tcf(c_148886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127804,c_768]) ).

tcf(c_148887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X1,X1),X4,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X1) ),
    inference(superposition,[status(thm)],[c_127804,c_763]) ).

tcf(c_148888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_127804,c_840]) ).

tcf(c_148889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),iPr_def_13,iPr_def_13),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127804,c_126501]) ).

tcf(c_148907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),tc_prod(X1,X2),tc_prod(X1,X2)),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_148883,c_127804]) ).

tcf(c_148910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_148879,c_127804]) ).

tcf(c_148934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_596,c_127828]) ).

tcf(c_148941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127828,c_562]) ).

tcf(c_148942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127828,c_561]) ).

tcf(c_148943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127828,c_565]) ).

tcf(c_148944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X5),
    inference(superposition,[status(thm)],[c_127828,c_144852]) ).

tcf(c_148945,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127828,c_125973]) ).

tcf(c_148946,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127828,c_125887]) ).

tcf(c_148947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127828,c_633]) ).

tcf(c_148948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127828,c_776]) ).

tcf(c_148949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127828,c_762]) ).

tcf(c_148951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127828,c_642]) ).

tcf(c_148952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127828,c_774]) ).

tcf(c_148953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_127828,c_770]) ).

tcf(c_148954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127828,c_768]) ).

tcf(c_148955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X1,X1),X4,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X1) ),
    inference(superposition,[status(thm)],[c_127828,c_763]) ).

tcf(c_148956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_127828,c_840]) ).

tcf(c_148957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),iPr_def_13,iPr_def_13),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127828,c_126501]) ).

tcf(c_148975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),tc_prod(X1,X2),tc_prod(X1,X2)),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_148951,c_127828]) ).

tcf(c_148978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_148947,c_127828]) ).

tcf(c_149106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_596,c_127837]) ).

tcf(c_149113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127837,c_562]) ).

tcf(c_149114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127837,c_561]) ).

tcf(c_149115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127837,c_565]) ).

tcf(c_149116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X5),
    inference(superposition,[status(thm)],[c_127837,c_144852]) ).

tcf(c_149117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127837,c_125973]) ).

tcf(c_149118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127837,c_125887]) ).

tcf(c_149119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127837,c_633]) ).

tcf(c_149120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127837,c_776]) ).

tcf(c_149121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127837,c_762]) ).

tcf(c_149123,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127837,c_642]) ).

tcf(c_149124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127837,c_774]) ).

tcf(c_149125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_127837,c_770]) ).

tcf(c_149126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127837,c_768]) ).

tcf(c_149127,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X1,X1),X4,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X1) ),
    inference(superposition,[status(thm)],[c_127837,c_763]) ).

tcf(c_149128,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_127837,c_840]) ).

tcf(c_149129,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),iPr_def_13,iPr_def_13),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127837,c_126501]) ).

tcf(c_149147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),tc_prod(X1,X2),tc_prod(X1,X2)),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_149123,c_127837]) ).

tcf(c_149150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_149119,c_127837]) ).

tcf(c_149167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_687,c_127838]) ).

tcf(c_149174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127838,c_562]) ).

tcf(c_149175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X4,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_127838,c_561]) ).

tcf(c_149176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127838,c_565]) ).

tcf(c_149177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X5),
    inference(superposition,[status(thm)],[c_127838,c_144852]) ).

tcf(c_149178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127838,c_125973]) ).

tcf(c_149179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X4)),
    inference(superposition,[status(thm)],[c_127838,c_125887]) ).

tcf(c_149180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_127838,c_633]) ).

tcf(c_149181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_127838,c_776]) ).

tcf(c_149182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_127838,c_762]) ).

tcf(c_149184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_127838,c_642]) ).

tcf(c_149185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_127838,c_774]) ).

tcf(c_149186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_127838,c_770]) ).

tcf(c_149187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_127838,c_768]) ).

tcf(c_149188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X5,X1,X1),X4,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X1) ),
    inference(superposition,[status(thm)],[c_127838,c_763]) ).

tcf(c_149189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4)),
    inference(superposition,[status(thm)],[c_127838,c_840]) ).

tcf(c_149190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),iPr_def_13,iPr_def_13),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_127838,c_126501]) ).

tcf(c_149208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X5 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),tc_prod(X1,X2),tc_prod(X1,X2)),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_149184,c_127838]) ).

tcf(c_149211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_149180,c_127838]) ).

tcf(c_149274,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128087,c_841]) ).

tcf(c_149279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_579,c_7263,c_7265]) ).

tcf(c_149280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6),
    inference(superposition,[status(thm)],[c_149279,c_144852]) ).

tcf(c_149281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,X3,c_Expr_Oexp_Othrow(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149279,c_125973]) ).

tcf(c_149282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,X3,c_Expr_Oexp_Othrow(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149279,c_125887]) ).

tcf(c_149283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,X6,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149279,c_633]) ).

tcf(c_149284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,X5,c_Expr_Oexp_Othrow(X0,iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149279,c_776]) ).

tcf(c_149286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,X4,c_Expr_Oexp_Othrow(X5,iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149279,c_761]) ).

tcf(c_149287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X5 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149279,c_642]) ).

tcf(c_149288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X6),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149279,c_774]) ).

tcf(c_149290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,X2,c_Expr_Oexp_Othrow(X3,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149279,c_768]) ).

tcf(c_149291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,X4,c_Expr_Oexp_Othrow(X5,iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,X4,c_Expr_Oexp_Othrow(X5,iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149279,c_763]) ).

tcf(c_149292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X1,iPr_def_10),X2,X3,c_Expr_Oexp_Othrow(X4,iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149279,c_840]) ).

tcf(c_149320,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,X0,X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_842,c_7263,c_7265]) ).

tcf(c_149348,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_465,c_7263,c_7265]) ).

tcf(c_149349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5),
    inference(superposition,[status(thm)],[c_149348,c_144852]) ).

tcf(c_149350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149348,c_125973]) ).

tcf(c_149351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149348,c_125887]) ).

tcf(c_149352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X4,X5,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149348,c_633]) ).

tcf(c_149353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X3,X4,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149348,c_776]) ).

tcf(c_149354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149348,c_762]) ).

tcf(c_149355,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149348,c_761]) ).

tcf(c_149356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X4 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149348,c_642]) ).

tcf(c_149357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X5),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X4,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149348,c_774]) ).

tcf(c_149358,plain,
    ! [X0: $i,X1: $i,X2: $i] : c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149348,c_770]) ).

tcf(c_149359,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X2),iPr_def_10),iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149348,c_768]) ).

tcf(c_149360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149348,c_763]) ).

tcf(c_149361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149348,c_840]) ).

tcf(c_149408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_536,c_7263,c_7265]) ).

tcf(c_149409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X4),
    inference(superposition,[status(thm)],[c_149408,c_144852]) ).

tcf(c_149410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OWhile(X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X1,c_Expr_Oexp_OSeq(X2,c_Expr_Oexp_OWhile(X1,X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149408,c_125973]) ).

tcf(c_149411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OWhile(X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X1,c_Expr_Oexp_OSeq(X2,c_Expr_Oexp_OWhile(X1,X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149408,c_125887]) ).

tcf(c_149412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149408,c_633]) ).

tcf(c_149413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149408,c_776]) ).

tcf(c_149414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X2,c_Expr_Oexp_OSeq(X3,c_Expr_Oexp_OWhile(X2,X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149408,c_762]) ).

tcf(c_149415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OWhile(X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149408,c_761]) ).

tcf(c_149416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X3 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149408,c_642]) ).

tcf(c_149417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X3,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149408,c_774]) ).

tcf(c_149418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Expr_Oexp_OCond(X0,c_Expr_Oexp_OSeq(X1,c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149408,c_770]) ).

tcf(c_149419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : c_in(c_Pair(c_Expr_Oexp_OWhile(X0,X1,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149408,c_768]) ).

tcf(c_149420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,c_Expr_Oexp_OSeq(X3,c_Expr_Oexp_OWhile(X2,X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OWhile(X2,X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,c_Expr_Oexp_OSeq(X3,c_Expr_Oexp_OWhile(X2,X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149408,c_763]) ).

tcf(c_149421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OWhile(X1,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X1,c_Expr_Oexp_OSeq(X2,c_Expr_Oexp_OWhile(X1,X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(c_Value_Oval_OUnit,iPr_def_10),iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149408,c_840]) ).

tcf(c_149483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128103,c_841]) ).

tcf(c_149496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128119,c_841]) ).

tcf(c_149506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128136,c_841]) ).

tcf(c_149515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128153,c_841]) ).

tcf(c_149531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128211,c_841]) ).

tcf(c_149555,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_128233,c_841]) ).

tcf(c_149561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_559,c_7263,c_7265]) ).

tcf(c_149562,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6),
    inference(superposition,[status(thm)],[c_149561,c_144852]) ).

tcf(c_149563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149561,c_125973]) ).

tcf(c_149564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149561,c_125887]) ).

tcf(c_149565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X4,X5,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X4,c_Expr_Oexp_OVal(X6,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X0,iPr_def_10),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149561,c_633]) ).

tcf(c_149566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X3,X4,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X3,c_Expr_Oexp_OVal(X5,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X0,iPr_def_10),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OVal(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149561,c_776]) ).

tcf(c_149568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X5,iPr_def_10),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149561,c_761]) ).

tcf(c_149569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X5 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149561,c_642]) ).

tcf(c_149570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OVal(X3,iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X6),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149561,c_774]) ).

tcf(c_149572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149561,c_768]) ).

tcf(c_149573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X5,iPr_def_10),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X5,iPr_def_10),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149561,c_763]) ).

tcf(c_149574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X4,iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149561,c_840]) ).

tcf(c_149601,plain,
    c_in(c_Pair(c_Pair(v_e,v_s,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(v_e_H,v_s_H,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_863,c_7263,c_7265]) ).

tcf(c_149630,plain,
    c_in(c_Pair(v_e,v_s,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149601,c_768]) ).

tcf(c_149633,plain,
    ! [X0: $i] : c_in(c_Pair(c_Pair(v_e,v_s,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(v_e_H,v_s_H,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(v_P),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X0),
    inference(superposition,[status(thm)],[c_149601,c_136744]) ).

tcf(c_149650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X5),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),
    inference(light_normalisation,[status(thm)],[c_468,c_7263,c_7265]) ).

tcf(c_149651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6),
    inference(superposition,[status(thm)],[c_149650,c_144852]) ).

tcf(c_149652,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149650,c_125973]) ).

tcf(c_149653,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X0),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149650,c_125887]) ).

tcf(c_149654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X4,X5,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X4,c_Expr_Oexp_OVal(X6,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X2,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X3),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149650,c_633]) ).

tcf(c_149655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X3,X4,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X3,c_Expr_Oexp_OVal(X5,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X0),iPr_def_10),iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X2),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149650,c_776]) ).

tcf(c_149657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X5),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X0,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X0,c_SmallStep_Ored(X1),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149650,c_761]) ).

tcf(c_149658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X5 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149650,c_642]) ).

tcf(c_149659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X6),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))) ),
    inference(superposition,[status(thm)],[c_149650,c_774]) ).

tcf(c_149661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(c_Expr_Oexp_OBlock(X0,X1,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X0,c_Expr_Oexp_OVal(X2,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X3),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X4,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X5),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),
    inference(superposition,[status(thm)],[c_149650,c_768]) ).

tcf(c_149662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X5),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X5),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X2,X3,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X2,c_Expr_Oexp_OVal(X4,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X5),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X5),iPr_def_10),iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X1,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X0),X1,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149650,c_763]) ).

tcf(c_149663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_SmallStep_Ored(X0),c_Pair(c_Pair(c_Expr_Oexp_OBlock(X1,X2,c_Expr_Oexp_OSeq(c_Expr_Oexp_OLAss(X1,c_Expr_Oexp_OVal(X3,iPr_def_10),iPr_def_10),c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(c_Expr_Oexp_OVal(c_Value_Oval_OAddr(X4),iPr_def_10),iPr_def_10),X5,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))),
    inference(superposition,[status(thm)],[c_149650,c_840]) ).

tcf(c_149692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_Objects_Ohext(X1,X4)
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_570,c_7263,c_7265]) ).

tcf(c_149729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128259,c_841]) ).

tcf(c_149738,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128282,c_841]) ).

tcf(c_149754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128308,c_841]) ).

tcf(c_149761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128336,c_841]) ).

tcf(c_149771,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128353,c_841]) ).

tcf(c_149797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128379,c_841]) ).

tcf(c_149803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_819,c_7263,c_7265]) ).

tcf(c_149810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_144852]) ).

tcf(c_149811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_125973]) ).

tcf(c_149812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_125887]) ).

tcf(c_149813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_633]) ).

tcf(c_149814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_776]) ).

tcf(c_149815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_762]) ).

tcf(c_149816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_761]) ).

tcf(c_149817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X5 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_642]) ).

tcf(c_149818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_774]) ).

tcf(c_149819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_770]) ).

tcf(c_149820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_768]) ).

tcf(c_149821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_763]) ).

tcf(c_149822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_840]) ).

tcf(c_149823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_Othrow(X0,iPr_def_10),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149803,c_149320]) ).

tcf(c_149895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_817,c_7263,c_7265]) ).

tcf(c_149902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_144852]) ).

tcf(c_149903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_125973]) ).

tcf(c_149904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_125887]) ).

tcf(c_149905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_633]) ).

tcf(c_149906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_776]) ).

tcf(c_149907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_762]) ).

tcf(c_149908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_761]) ).

tcf(c_149909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X6 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_642]) ).

tcf(c_149910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_774]) ).

tcf(c_149911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_770]) ).

tcf(c_149912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_768]) ).

tcf(c_149913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_763]) ).

tcf(c_149914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_840]) ).

tcf(c_149915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OLAss(X6,X0,iPr_def_10),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_149895,c_149320]) ).

tcf(c_150052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_818,c_7263,c_7265]) ).

tcf(c_150059,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_144852]) ).

tcf(c_150060,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_125973]) ).

tcf(c_150061,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_125887]) ).

tcf(c_150062,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_633]) ).

tcf(c_150063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_776]) ).

tcf(c_150064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X2,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_762]) ).

tcf(c_150065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X0,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_761]) ).

tcf(c_150066,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X6 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_642]) ).

tcf(c_150067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_774]) ).

tcf(c_150068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_770]) ).

tcf(c_150069,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_768]) ).

tcf(c_150070,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_763]) ).

tcf(c_150071,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_840]) ).

tcf(c_150072,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OSeq(X0,X6,iPr_def_10),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150052,c_149320]) ).

tcf(c_150177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_823,c_7263,c_7265]) ).

tcf(c_150184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_144852]) ).

tcf(c_150185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_125973]) ).

tcf(c_150186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_125887]) ).

tcf(c_150187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_633]) ).

tcf(c_150188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_776]) ).

tcf(c_150189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_762]) ).

tcf(c_150190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_761]) ).

tcf(c_150191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X6 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_642]) ).

tcf(c_150192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X6,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_774]) ).

tcf(c_150193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_770]) ).

tcf(c_150194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_768]) ).

tcf(c_150195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCast(X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCast(X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_763]) ).

tcf(c_150196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_840]) ).

tcf(c_150197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OCast(X6,X0,iPr_def_10),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150177,c_149320]) ).

tcf(c_150318,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128408,c_841]) ).

tcf(c_150325,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128443,c_841]) ).

tcf(c_150335,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128460,c_841]) ).

tcf(c_150344,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_128477,c_841]) ).

tcf(c_150352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_129343,c_841]) ).

tcf(c_150357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),
    inference(superposition,[status(thm)],[c_129370,c_841]) ).

tcf(c_150364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_815,c_7263,c_7265]) ).

tcf(c_150371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_144852]) ).

tcf(c_150372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_125973]) ).

tcf(c_150373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_125887]) ).

tcf(c_150374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_633]) ).

tcf(c_150375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_776]) ).

tcf(c_150376,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_762]) ).

tcf(c_150377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_761]) ).

tcf(c_150378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X7 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_642]) ).

tcf(c_150379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_774]) ).

tcf(c_150380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_770]) ).

tcf(c_150381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_768]) ).

tcf(c_150382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_763]) ).

tcf(c_150383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_840]) ).

tcf(c_150384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OBinOp(X0,X6,X7,iPr_def_10),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150364,c_149320]) ).

tcf(c_150442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_816,c_7263,c_7265]) ).

tcf(c_150449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_144852]) ).

tcf(c_150450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_125973]) ).

tcf(c_150451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_125887]) ).

tcf(c_150452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_633]) ).

tcf(c_150453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_776]) ).

tcf(c_150454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_762]) ).

tcf(c_150455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_761]) ).

tcf(c_150456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X7 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_642]) ).

tcf(c_150457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_774]) ).

tcf(c_150458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_770]) ).

tcf(c_150459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_768]) ).

tcf(c_150460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_763]) ).

tcf(c_150461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_840]) ).

tcf(c_150462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OCall(X0,X6,X7,iPr_def_10),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150442,c_149320]) ).

tcf(c_150826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_820,c_7263,c_7265]) ).

tcf(c_150833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_144852]) ).

tcf(c_150834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_125973]) ).

tcf(c_150835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_125887]) ).

tcf(c_150836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_633]) ).

tcf(c_150837,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_776]) ).

tcf(c_150838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_762]) ).

tcf(c_150839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_761]) ).

tcf(c_150840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X7 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_642]) ).

tcf(c_150841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_774]) ).

tcf(c_150842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_770]) ).

tcf(c_150843,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_768]) ).

tcf(c_150844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_763]) ).

tcf(c_150845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_840]) ).

tcf(c_150846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OFAcc(X0,X6,X7,iPr_def_10),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150826,c_149320]) ).

tcf(c_150886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_825,c_7263,c_7265]) ).

tcf(c_150893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_144852]) ).

tcf(c_150894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_125973]) ).

tcf(c_150895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_125887]) ).

tcf(c_150896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_633]) ).

tcf(c_150897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_776]) ).

tcf(c_150898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_762]) ).

tcf(c_150899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_761]) ).

tcf(c_150900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X7 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_642]) ).

tcf(c_150901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_774]) ).

tcf(c_150902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_770]) ).

tcf(c_150903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_768]) ).

tcf(c_150904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_763]) ).

tcf(c_150905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_840]) ).

tcf(c_150906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OCond(X0,X6,X7,iPr_def_10),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_150886,c_149320]) ).

tcf(c_150961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_129497,c_841]) ).

tcf(c_150972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_129536,c_841]) ).

tcf(c_150974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X3,X4),X5),X6),
    inference(superposition,[status(thm)],[c_129954,c_841]) ).

tcf(c_150984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_129976,c_841]) ).

tcf(c_150985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X2),X3),X4)),
    inference(superposition,[status(thm)],[c_743,c_129996]) ).

tcf(c_150991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X2),X3),X4)),
    inference(superposition,[status(thm)],[c_743,c_129997]) ).

tcf(c_150996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_129997,c_841]) ).

tcf(c_151010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_130019,c_841]) ).

tcf(c_151033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_821,c_7263,c_7265]) ).

tcf(c_151040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_144852]) ).

tcf(c_151041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_125973]) ).

tcf(c_151042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_125887]) ).

tcf(c_151043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_633]) ).

tcf(c_151044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_776]) ).

tcf(c_151045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X2,X6,X7,X8,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_762]) ).

tcf(c_151046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X0,X6,X7,X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_761]) ).

tcf(c_151047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X8 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_642]) ).

tcf(c_151048,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_774]) ).

tcf(c_151049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_770]) ).

tcf(c_151050,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_768]) ).

tcf(c_151051,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X6,X7,X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X6,X7,X8,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X6,X7,X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X6,X7,X8,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_763]) ).

tcf(c_151052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_840]) ).

tcf(c_151053,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OFAss(X0,X6,X7,X8,iPr_def_10),X9)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151033,c_149320]) ).

tcf(c_151098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_824,c_7263,c_7265]) ).

tcf(c_151105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_144852]) ).

tcf(c_151106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_125973]) ).

tcf(c_151107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_125887]) ).

tcf(c_151108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_633]) ).

tcf(c_151109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_776]) ).

tcf(c_151110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X2,X6,X7,X8,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_762]) ).

tcf(c_151111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X0,X6,X7,X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_761]) ).

tcf(c_151112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X8 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_642]) ).

tcf(c_151113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_774]) ).

tcf(c_151114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_770]) ).

tcf(c_151115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_768]) ).

tcf(c_151116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X6,X7,X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X6,X7,X8,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X6,X7,X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X6,X7,X8,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_763]) ).

tcf(c_151117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_840]) ).

tcf(c_151118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OTryCatch(X0,X6,X7,X8,iPr_def_10),X9)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151098,c_149320]) ).

tcf(c_151183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_571,c_7263,c_7265]) ).

tcf(c_151190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_144852]) ).

tcf(c_151191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_125973]) ).

tcf(c_151192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_125887]) ).

tcf(c_151193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_633]) ).

tcf(c_151194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_776]) ).

tcf(c_151195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_762]) ).

tcf(c_151196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_761]) ).

tcf(c_151197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X7 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_642]) ).

tcf(c_151198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_774]) ).

tcf(c_151199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_770]) ).

tcf(c_151200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_768]) ).

tcf(c_151201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_763]) ).

tcf(c_151202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_840]) ).

tcf(c_151203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X0,iPr_def_10),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151183,c_149320]) ).

tcf(c_151275,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_572,c_7263,c_7265]) ).

tcf(c_151282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_144852]) ).

tcf(c_151283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_125973]) ).

tcf(c_151284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_125887]) ).

tcf(c_151285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_633]) ).

tcf(c_151286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_776]) ).

tcf(c_151287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_762]) ).

tcf(c_151288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X5,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X5,c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_761]) ).

tcf(c_151289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X8 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_642]) ).

tcf(c_151290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X4),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_774]) ).

tcf(c_151291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_770]) ).

tcf(c_151292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_768]) ).

tcf(c_151293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X5,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X4),X5,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_763]) ).

tcf(c_151294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X4),c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_840]) ).

tcf(c_151295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X4,X5,X3)
      | ~ c_TypeSafe__Mirabelle_Osconf(X4,X5,X1)
      | ~ c_WellTypeRT_OWTrt(X4,c_State_Ohp(X1),X5,c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X6,iPr_def_10),X7,X8,X0,iPr_def_10),X9)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X4),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151275,c_149320]) ).

tcf(c_151352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),
    inference(superposition,[status(thm)],[c_130097,c_841]) ).

tcf(c_151353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_687,c_130118]) ).

tcf(c_151354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_698,c_130118]) ).

tcf(c_151360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1),X2),X3)),
    inference(light_normalisation,[status(thm)],[c_151354,c_596]) ).

tcf(c_151361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X1,X1),X2),X3)),
    inference(light_normalisation,[status(thm)],[c_151353,c_596]) ).

tcf(c_151362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_687,c_130119]) ).

tcf(c_151363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_698,c_130119]) ).

tcf(c_151368,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_130119,c_841]) ).

tcf(c_151369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1),X2),X3)),
    inference(light_normalisation,[status(thm)],[c_151363,c_596]) ).

tcf(c_151370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X1,X1),X2),X3)),
    inference(light_normalisation,[status(thm)],[c_151362,c_596]) ).

tcf(c_151371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_596,c_130141]) ).

tcf(c_151378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X1,X1),X2),X3)),
    inference(light_normalisation,[status(thm)],[c_151371,c_596]) ).

tcf(c_151391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1),X1,X1),X2),X3)),
    inference(superposition,[status(thm)],[c_596,c_130142]) ).

tcf(c_151397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),
    inference(superposition,[status(thm)],[c_130142,c_841]) ).

tcf(c_151398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X1,X1),X2),X3)),
    inference(light_normalisation,[status(thm)],[c_151391,c_596]) ).

tcf(c_151431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135153,c_517]) ).

tcf(c_151432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_135153,c_537]) ).

tcf(c_151445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135154,c_517]) ).

tcf(c_151446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_135154,c_537]) ).

tcf(c_151447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_135154,c_841]) ).

tcf(c_151461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135296,c_517]) ).

tcf(c_151462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_135296,c_537]) ).

tcf(c_151470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_835,c_7263,c_7265]) ).

tcf(c_151505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151470,c_768]) ).

tcf(c_151508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151470,c_136744]) ).

tcf(c_151535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_828,c_7263,c_7265]) ).

tcf(c_151570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151535,c_768]) ).

tcf(c_151573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OLAss(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151535,c_136744]) ).

tcf(c_151600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_831,c_7263,c_7265]) ).

tcf(c_151635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151600,c_768]) ).

tcf(c_151638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCast(X5,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151600,c_136744]) ).

tcf(c_151665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_833,c_7263,c_7265]) ).

tcf(c_151700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151665,c_768]) ).

tcf(c_151703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OSeq(X2,X5,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_151665,c_136744]) ).

tcf(c_151734,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1),X2,X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_135297,c_517]) ).

tcf(c_151735,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2),X3,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_135297,c_537]) ).

tcf(c_151736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_135297,c_841]) ).

tcf(c_151761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145010,c_560]) ).

tcf(c_151762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145010,c_564]) ).

tcf(c_151763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145010,c_562]) ).

tcf(c_151764,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145010,c_561]) ).

tcf(c_151765,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_145010,c_565]) ).

tcf(c_151766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145010,c_144852]) ).

tcf(c_151767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145010,c_125973]) ).

tcf(c_151768,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145010,c_125887]) ).

tcf(c_151776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145010,c_849]) ).

tcf(c_151787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145010,c_633]) ).

tcf(c_151789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_145010,c_762]) ).

tcf(c_151791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145010,c_642]) ).

tcf(c_151792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145010,c_774]) ).

tcf(c_151793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145010,c_770]) ).

tcf(c_151794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145010,c_768]) ).

tcf(c_151795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_145010,c_763]) ).

tcf(c_151844,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151794,c_562]) ).

tcf(c_151845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151794,c_561]) ).

tcf(c_151846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_151794,c_565]) ).

tcf(c_151847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_151794,c_144852]) ).

tcf(c_151848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_151794,c_125973]) ).

tcf(c_151849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_151794,c_125887]) ).

tcf(c_151850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151794,c_633]) ).

tcf(c_151851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_151794,c_776]) ).

tcf(c_151852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_151794,c_762]) ).

tcf(c_151854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151794,c_642]) ).

tcf(c_151855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151794,c_774]) ).

tcf(c_151856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_151794,c_770]) ).

tcf(c_151857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_151794,c_768]) ).

tcf(c_151858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_151794,c_763]) ).

tcf(c_151859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_151794,c_840]) ).

tcf(c_151860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_151794,c_126501]) ).

tcf(c_151878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_151854,c_151794]) ).

tcf(c_151881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_151850,c_151794]) ).

tcf(c_151922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_151859,c_841]) ).

tcf(c_151929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151922,c_562]) ).

tcf(c_151930,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151922,c_561]) ).

tcf(c_151931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_151922,c_565]) ).

tcf(c_151932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_151922,c_144852]) ).

tcf(c_151933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_151922,c_125973]) ).

tcf(c_151934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_151922,c_125887]) ).

tcf(c_151935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151922,c_633]) ).

tcf(c_151936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_151922,c_776]) ).

tcf(c_151937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_151922,c_762]) ).

tcf(c_151939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151922,c_642]) ).

tcf(c_151940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151922,c_774]) ).

tcf(c_151941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_151922,c_770]) ).

tcf(c_151942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_151922,c_768]) ).

tcf(c_151943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_151922,c_763]) ).

tcf(c_151963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_151939,c_151922]) ).

tcf(c_151966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_151935,c_151922]) ).

tcf(c_151997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145011,c_144852]) ).

tcf(c_151998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145011,c_125973]) ).

tcf(c_151999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145011,c_125887]) ).

tcf(c_152000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_793]) ).

tcf(c_152001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145011,c_632]) ).

tcf(c_152002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145011,c_631]) ).

tcf(c_152003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_847]) ).

tcf(c_152004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145011,c_799]) ).

tcf(c_152005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_798]) ).

tcf(c_152006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145011,c_795]) ).

tcf(c_152007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_849]) ).

tcf(c_152008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_848]) ).

tcf(c_152010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_781]) ).

tcf(c_152011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145011,c_794]) ).

tcf(c_152012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145011,c_784]) ).

tcf(c_152013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145011,c_800]) ).

tcf(c_152014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145011,c_786]) ).

tcf(c_152015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145011,c_789]) ).

tcf(c_152017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145011,c_806]) ).

tcf(c_152018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145011,c_633]) ).

tcf(c_152019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145011,c_776]) ).

tcf(c_152020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145011,c_762]) ).

tcf(c_152021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145011,c_761]) ).

tcf(c_152022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145011,c_642]) ).

tcf(c_152023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145011,c_774]) ).

tcf(c_152024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145011,c_770]) ).

tcf(c_152025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145011,c_768]) ).

tcf(c_152026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145011,c_763]) ).

tcf(c_152149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145012,c_144852]) ).

tcf(c_152150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145012,c_125973]) ).

tcf(c_152151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145012,c_125887]) ).

tcf(c_152152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_793]) ).

tcf(c_152153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145012,c_632]) ).

tcf(c_152154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145012,c_631]) ).

tcf(c_152155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_847]) ).

tcf(c_152156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145012,c_799]) ).

tcf(c_152157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_798]) ).

tcf(c_152158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145012,c_795]) ).

tcf(c_152159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_849]) ).

tcf(c_152160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_848]) ).

tcf(c_152162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_781]) ).

tcf(c_152163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145012,c_794]) ).

tcf(c_152164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145012,c_784]) ).

tcf(c_152165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145012,c_800]) ).

tcf(c_152166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145012,c_786]) ).

tcf(c_152167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145012,c_789]) ).

tcf(c_152169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145012,c_806]) ).

tcf(c_152170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145012,c_633]) ).

tcf(c_152171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145012,c_776]) ).

tcf(c_152172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145012,c_762]) ).

tcf(c_152173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145012,c_761]) ).

tcf(c_152174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145012,c_642]) ).

tcf(c_152175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145012,c_774]) ).

tcf(c_152176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145012,c_770]) ).

tcf(c_152177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145012,c_768]) ).

tcf(c_152178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145012,c_763]) ).

tcf(c_152285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145035,c_560]) ).

tcf(c_152286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145035,c_564]) ).

tcf(c_152287,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145035,c_562]) ).

tcf(c_152288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145035,c_561]) ).

tcf(c_152289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_145035,c_565]) ).

tcf(c_152290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145035,c_144852]) ).

tcf(c_152291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145035,c_125973]) ).

tcf(c_152292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145035,c_125887]) ).

tcf(c_152300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145035,c_849]) ).

tcf(c_152311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145035,c_633]) ).

tcf(c_152313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_145035,c_762]) ).

tcf(c_152315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145035,c_642]) ).

tcf(c_152316,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145035,c_774]) ).

tcf(c_152317,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145035,c_770]) ).

tcf(c_152318,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145035,c_768]) ).

tcf(c_152319,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_145035,c_763]) ).

tcf(c_152416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_152318,c_562]) ).

tcf(c_152417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_152318,c_561]) ).

tcf(c_152418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_152318,c_565]) ).

tcf(c_152419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_152318,c_144852]) ).

tcf(c_152420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_152318,c_125973]) ).

tcf(c_152421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_152318,c_125887]) ).

tcf(c_152422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_152318,c_633]) ).

tcf(c_152423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_152318,c_776]) ).

tcf(c_152424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_152318,c_762]) ).

tcf(c_152426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_152318,c_642]) ).

tcf(c_152427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_152318,c_774]) ).

tcf(c_152428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_152318,c_770]) ).

tcf(c_152429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_152318,c_768]) ).

tcf(c_152430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_152318,c_763]) ).

tcf(c_152431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_152318,c_840]) ).

tcf(c_152432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_152318,c_126501]) ).

tcf(c_152450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_152426,c_152318]) ).

tcf(c_152453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_152422,c_152318]) ).

tcf(c_152474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_152431,c_841]) ).

tcf(c_152482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_152474,c_562]) ).

tcf(c_152483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_152474,c_561]) ).

tcf(c_152484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_152474,c_565]) ).

tcf(c_152485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_152474,c_144852]) ).

tcf(c_152486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_152474,c_125973]) ).

tcf(c_152487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_152474,c_125887]) ).

tcf(c_152488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_152474,c_633]) ).

tcf(c_152489,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_152474,c_776]) ).

tcf(c_152490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_152474,c_762]) ).

tcf(c_152492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_152474,c_642]) ).

tcf(c_152493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_152474,c_774]) ).

tcf(c_152494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_152474,c_770]) ).

tcf(c_152495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_152474,c_768]) ).

tcf(c_152496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_152474,c_763]) ).

tcf(c_152516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_152492,c_152474]) ).

tcf(c_152519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_152488,c_152474]) ).

tcf(c_152568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145042,c_144852]) ).

tcf(c_152569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145042,c_125973]) ).

tcf(c_152570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145042,c_125887]) ).

tcf(c_152571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_793]) ).

tcf(c_152572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145042,c_632]) ).

tcf(c_152573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145042,c_631]) ).

tcf(c_152574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_847]) ).

tcf(c_152575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145042,c_799]) ).

tcf(c_152576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_798]) ).

tcf(c_152577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145042,c_795]) ).

tcf(c_152578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_849]) ).

tcf(c_152579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_848]) ).

tcf(c_152581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_781]) ).

tcf(c_152582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145042,c_794]) ).

tcf(c_152583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145042,c_784]) ).

tcf(c_152584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145042,c_800]) ).

tcf(c_152585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145042,c_786]) ).

tcf(c_152586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145042,c_789]) ).

tcf(c_152588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145042,c_806]) ).

tcf(c_152589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145042,c_633]) ).

tcf(c_152590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145042,c_776]) ).

tcf(c_152591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145042,c_762]) ).

tcf(c_152592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145042,c_761]) ).

tcf(c_152593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145042,c_642]) ).

tcf(c_152594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145042,c_774]) ).

tcf(c_152595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145042,c_770]) ).

tcf(c_152596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145042,c_768]) ).

tcf(c_152597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145042,c_763]) ).

tcf(c_152725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_830,c_7263,c_7265]) ).

tcf(c_152760,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152725,c_768]) ).

tcf(c_152763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_Othrow(X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152725,c_136744]) ).

tcf(c_152790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X4,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_558,c_7263,c_7265]) ).

tcf(c_152825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X4,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152790,c_768]) ).

tcf(c_152828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X4,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X5)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(c_Value_Oval_ONull,iPr_def_10),X2,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X3),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152790,c_136744]) ).

tcf(c_152855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_575,c_7263,c_7265]) ).

tcf(c_152890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OWhile(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152855,c_768]) ).

tcf(c_152893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OWhile(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152855,c_136744]) ).

tcf(c_152920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_653,c_7263,c_7265]) ).

tcf(c_152955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152920,c_768]) ).

tcf(c_152958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_152920,c_136744]) ).

tcf(c_152987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145043,c_144852]) ).

tcf(c_152988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145043,c_125973]) ).

tcf(c_152989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145043,c_125887]) ).

tcf(c_152990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_793]) ).

tcf(c_152991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145043,c_632]) ).

tcf(c_152992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145043,c_631]) ).

tcf(c_152993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_847]) ).

tcf(c_152994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145043,c_799]) ).

tcf(c_152995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_798]) ).

tcf(c_152996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145043,c_795]) ).

tcf(c_152997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_849]) ).

tcf(c_152998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_848]) ).

tcf(c_153000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_781]) ).

tcf(c_153001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145043,c_794]) ).

tcf(c_153002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145043,c_784]) ).

tcf(c_153003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145043,c_800]) ).

tcf(c_153004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145043,c_786]) ).

tcf(c_153005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145043,c_789]) ).

tcf(c_153007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145043,c_806]) ).

tcf(c_153008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145043,c_633]) ).

tcf(c_153009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145043,c_776]) ).

tcf(c_153010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145043,c_762]) ).

tcf(c_153011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145043,c_761]) ).

tcf(c_153012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145043,c_642]) ).

tcf(c_153013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145043,c_774]) ).

tcf(c_153014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145043,c_770]) ).

tcf(c_153015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145043,c_768]) ).

tcf(c_153016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145043,c_763]) ).

tcf(c_153135,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145044,c_560]) ).

tcf(c_153136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145044,c_564]) ).

tcf(c_153137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145044,c_562]) ).

tcf(c_153138,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145044,c_561]) ).

tcf(c_153139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_145044,c_565]) ).

tcf(c_153140,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145044,c_144852]) ).

tcf(c_153141,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145044,c_125973]) ).

tcf(c_153142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145044,c_125887]) ).

tcf(c_153150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145044,c_849]) ).

tcf(c_153161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145044,c_633]) ).

tcf(c_153163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_145044,c_762]) ).

tcf(c_153165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145044,c_642]) ).

tcf(c_153166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145044,c_774]) ).

tcf(c_153167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145044,c_770]) ).

tcf(c_153168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145044,c_768]) ).

tcf(c_153169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_145044,c_763]) ).

tcf(c_153249,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153168,c_562]) ).

tcf(c_153250,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153168,c_561]) ).

tcf(c_153251,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_153168,c_565]) ).

tcf(c_153252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_153168,c_144852]) ).

tcf(c_153253,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_153168,c_125973]) ).

tcf(c_153254,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_153168,c_125887]) ).

tcf(c_153255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_153168,c_633]) ).

tcf(c_153256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_153168,c_776]) ).

tcf(c_153257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_153168,c_762]) ).

tcf(c_153259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_153168,c_642]) ).

tcf(c_153260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_153168,c_774]) ).

tcf(c_153261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_153168,c_770]) ).

tcf(c_153262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_153168,c_768]) ).

tcf(c_153263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_153168,c_763]) ).

tcf(c_153264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_153168,c_840]) ).

tcf(c_153265,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_153168,c_126501]) ).

tcf(c_153283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_153259,c_153168]) ).

tcf(c_153286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_153255,c_153168]) ).

tcf(c_153320,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_153264,c_841]) ).

tcf(c_153328,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153320,c_562]) ).

tcf(c_153329,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153320,c_561]) ).

tcf(c_153330,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_153320,c_565]) ).

tcf(c_153331,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_153320,c_144852]) ).

tcf(c_153332,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_153320,c_125973]) ).

tcf(c_153333,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_153320,c_125887]) ).

tcf(c_153334,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_153320,c_633]) ).

tcf(c_153335,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_153320,c_776]) ).

tcf(c_153336,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_153320,c_762]) ).

tcf(c_153338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_153320,c_642]) ).

tcf(c_153339,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_153320,c_774]) ).

tcf(c_153340,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_153320,c_770]) ).

tcf(c_153341,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_153320,c_768]) ).

tcf(c_153342,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_153320,c_763]) ).

tcf(c_153362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_153338,c_153320]) ).

tcf(c_153365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_153334,c_153320]) ).

tcf(c_153429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145045,c_560]) ).

tcf(c_153430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145045,c_564]) ).

tcf(c_153431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145045,c_562]) ).

tcf(c_153432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145045,c_561]) ).

tcf(c_153433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_145045,c_565]) ).

tcf(c_153434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145045,c_144852]) ).

tcf(c_153435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145045,c_125973]) ).

tcf(c_153436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145045,c_125887]) ).

tcf(c_153444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145045,c_849]) ).

tcf(c_153455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145045,c_633]) ).

tcf(c_153457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_145045,c_762]) ).

tcf(c_153459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145045,c_642]) ).

tcf(c_153460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145045,c_774]) ).

tcf(c_153461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145045,c_770]) ).

tcf(c_153462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145045,c_768]) ).

tcf(c_153463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_145045,c_763]) ).

tcf(c_153529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153462,c_562]) ).

tcf(c_153530,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153462,c_561]) ).

tcf(c_153531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_153462,c_565]) ).

tcf(c_153532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_153462,c_144852]) ).

tcf(c_153533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_153462,c_125973]) ).

tcf(c_153534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_153462,c_125887]) ).

tcf(c_153535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_153462,c_633]) ).

tcf(c_153536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_153462,c_776]) ).

tcf(c_153537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_153462,c_762]) ).

tcf(c_153539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_153462,c_642]) ).

tcf(c_153540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_153462,c_774]) ).

tcf(c_153541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_153462,c_770]) ).

tcf(c_153542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_153462,c_768]) ).

tcf(c_153543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_153462,c_763]) ).

tcf(c_153544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_153462,c_840]) ).

tcf(c_153545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_153462,c_126501]) ).

tcf(c_153563,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_153539,c_153462]) ).

tcf(c_153566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_153535,c_153462]) ).

tcf(c_153616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_153544,c_841]) ).

tcf(c_153624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153616,c_562]) ).

tcf(c_153625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_153616,c_561]) ).

tcf(c_153626,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_153616,c_565]) ).

tcf(c_153627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_153616,c_144852]) ).

tcf(c_153628,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_153616,c_125973]) ).

tcf(c_153629,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_153616,c_125887]) ).

tcf(c_153630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_153616,c_633]) ).

tcf(c_153631,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_153616,c_776]) ).

tcf(c_153632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_153616,c_762]) ).

tcf(c_153634,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_153616,c_642]) ).

tcf(c_153635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_153616,c_774]) ).

tcf(c_153636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_153616,c_770]) ).

tcf(c_153637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_153616,c_768]) ).

tcf(c_153638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_153616,c_763]) ).

tcf(c_153658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_153634,c_153616]) ).

tcf(c_153661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_153630,c_153616]) ).

tcf(c_153959,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145046,c_144852]) ).

tcf(c_153960,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145046,c_125973]) ).

tcf(c_153961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145046,c_125887]) ).

tcf(c_153962,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_793]) ).

tcf(c_153963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145046,c_632]) ).

tcf(c_153964,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145046,c_631]) ).

tcf(c_153965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_847]) ).

tcf(c_153966,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145046,c_799]) ).

tcf(c_153967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_798]) ).

tcf(c_153968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145046,c_795]) ).

tcf(c_153969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_849]) ).

tcf(c_153970,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_848]) ).

tcf(c_153972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_781]) ).

tcf(c_153973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145046,c_794]) ).

tcf(c_153974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145046,c_784]) ).

tcf(c_153975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145046,c_800]) ).

tcf(c_153976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145046,c_786]) ).

tcf(c_153977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145046,c_789]) ).

tcf(c_153979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145046,c_806]) ).

tcf(c_153980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145046,c_633]) ).

tcf(c_153981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145046,c_776]) ).

tcf(c_153982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145046,c_762]) ).

tcf(c_153983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145046,c_761]) ).

tcf(c_153984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145046,c_642]) ).

tcf(c_153985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145046,c_774]) ).

tcf(c_153986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145046,c_770]) ).

tcf(c_153987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145046,c_768]) ).

tcf(c_153988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145046,c_763]) ).

tcf(c_154067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145048,c_144852]) ).

tcf(c_154068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145048,c_125973]) ).

tcf(c_154069,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145048,c_125887]) ).

tcf(c_154070,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_793]) ).

tcf(c_154071,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145048,c_632]) ).

tcf(c_154072,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145048,c_631]) ).

tcf(c_154073,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_847]) ).

tcf(c_154074,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145048,c_799]) ).

tcf(c_154075,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_798]) ).

tcf(c_154076,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145048,c_795]) ).

tcf(c_154077,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_849]) ).

tcf(c_154078,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_848]) ).

tcf(c_154080,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_781]) ).

tcf(c_154081,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145048,c_794]) ).

tcf(c_154082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145048,c_784]) ).

tcf(c_154083,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145048,c_800]) ).

tcf(c_154084,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145048,c_786]) ).

tcf(c_154085,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145048,c_789]) ).

tcf(c_154087,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145048,c_806]) ).

tcf(c_154088,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145048,c_633]) ).

tcf(c_154089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145048,c_776]) ).

tcf(c_154090,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145048,c_762]) ).

tcf(c_154091,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145048,c_761]) ).

tcf(c_154092,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145048,c_642]) ).

tcf(c_154093,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145048,c_774]) ).

tcf(c_154094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145048,c_770]) ).

tcf(c_154095,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145048,c_768]) ).

tcf(c_154096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145048,c_763]) ).

tcf(c_154186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145049,c_144852]) ).

tcf(c_154187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145049,c_125973]) ).

tcf(c_154188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145049,c_125887]) ).

tcf(c_154189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_793]) ).

tcf(c_154190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145049,c_632]) ).

tcf(c_154191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145049,c_631]) ).

tcf(c_154192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_847]) ).

tcf(c_154193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145049,c_799]) ).

tcf(c_154194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_798]) ).

tcf(c_154195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145049,c_795]) ).

tcf(c_154196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_849]) ).

tcf(c_154197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_848]) ).

tcf(c_154199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_781]) ).

tcf(c_154200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145049,c_794]) ).

tcf(c_154201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145049,c_784]) ).

tcf(c_154202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145049,c_800]) ).

tcf(c_154203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145049,c_786]) ).

tcf(c_154204,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145049,c_789]) ).

tcf(c_154206,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145049,c_806]) ).

tcf(c_154207,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145049,c_633]) ).

tcf(c_154208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145049,c_776]) ).

tcf(c_154209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145049,c_762]) ).

tcf(c_154210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145049,c_761]) ).

tcf(c_154211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145049,c_642]) ).

tcf(c_154212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145049,c_774]) ).

tcf(c_154213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145049,c_770]) ).

tcf(c_154214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145049,c_768]) ).

tcf(c_154215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145049,c_763]) ).

tcf(c_154316,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_655,c_7263,c_7265]) ).

tcf(c_154351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154316,c_768]) ).

tcf(c_154354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OLAss(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154316,c_136744]) ).

tcf(c_154381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_656,c_7263,c_7265]) ).

tcf(c_154416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154381,c_768]) ).

tcf(c_154419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCast(X5,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X6)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154381,c_136744]) ).

tcf(c_154446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_827,c_7263,c_7265]) ).

tcf(c_154481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154446,c_768]) ).

tcf(c_154484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154446,c_136744]) ).

tcf(c_154511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_832,c_7263,c_7265]) ).

tcf(c_154546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154511,c_768]) ).

tcf(c_154549,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCall(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_154511,c_136744]) ).

tcf(c_154579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145050,c_144852]) ).

tcf(c_154580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145050,c_125973]) ).

tcf(c_154581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145050,c_125887]) ).

tcf(c_154582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_793]) ).

tcf(c_154583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145050,c_632]) ).

tcf(c_154584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145050,c_631]) ).

tcf(c_154585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_847]) ).

tcf(c_154586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145050,c_799]) ).

tcf(c_154587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_798]) ).

tcf(c_154588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145050,c_795]) ).

tcf(c_154589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_849]) ).

tcf(c_154590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_848]) ).

tcf(c_154592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_781]) ).

tcf(c_154593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145050,c_794]) ).

tcf(c_154594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145050,c_784]) ).

tcf(c_154595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145050,c_800]) ).

tcf(c_154596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145050,c_786]) ).

tcf(c_154597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145050,c_789]) ).

tcf(c_154599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145050,c_806]) ).

tcf(c_154600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145050,c_633]) ).

tcf(c_154601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145050,c_776]) ).

tcf(c_154602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145050,c_762]) ).

tcf(c_154603,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145050,c_761]) ).

tcf(c_154604,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145050,c_642]) ).

tcf(c_154605,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145050,c_774]) ).

tcf(c_154606,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145050,c_770]) ).

tcf(c_154607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145050,c_768]) ).

tcf(c_154608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145050,c_763]) ).

tcf(c_154729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145051,c_144852]) ).

tcf(c_154730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145051,c_125973]) ).

tcf(c_154731,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145051,c_125887]) ).

tcf(c_154732,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_793]) ).

tcf(c_154733,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145051,c_632]) ).

tcf(c_154734,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145051,c_631]) ).

tcf(c_154735,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_847]) ).

tcf(c_154736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145051,c_799]) ).

tcf(c_154737,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_798]) ).

tcf(c_154738,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145051,c_795]) ).

tcf(c_154739,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_849]) ).

tcf(c_154740,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_848]) ).

tcf(c_154742,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_781]) ).

tcf(c_154743,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145051,c_794]) ).

tcf(c_154744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145051,c_784]) ).

tcf(c_154745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145051,c_800]) ).

tcf(c_154746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145051,c_786]) ).

tcf(c_154747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145051,c_789]) ).

tcf(c_154749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145051,c_806]) ).

tcf(c_154750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145051,c_633]) ).

tcf(c_154751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145051,c_776]) ).

tcf(c_154752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145051,c_762]) ).

tcf(c_154753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145051,c_761]) ).

tcf(c_154754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145051,c_642]) ).

tcf(c_154755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145051,c_774]) ).

tcf(c_154756,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145051,c_770]) ).

tcf(c_154757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145051,c_768]) ).

tcf(c_154758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145051,c_763]) ).

tcf(c_154888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145052,c_144852]) ).

tcf(c_154889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145052,c_125973]) ).

tcf(c_154890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145052,c_125887]) ).

tcf(c_154891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_793]) ).

tcf(c_154892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145052,c_632]) ).

tcf(c_154893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145052,c_631]) ).

tcf(c_154894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_847]) ).

tcf(c_154895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145052,c_799]) ).

tcf(c_154896,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_798]) ).

tcf(c_154897,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145052,c_795]) ).

tcf(c_154898,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_849]) ).

tcf(c_154899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_848]) ).

tcf(c_154901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_781]) ).

tcf(c_154902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145052,c_794]) ).

tcf(c_154903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145052,c_784]) ).

tcf(c_154904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145052,c_800]) ).

tcf(c_154905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145052,c_786]) ).

tcf(c_154906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145052,c_789]) ).

tcf(c_154908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145052,c_806]) ).

tcf(c_154909,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145052,c_633]) ).

tcf(c_154910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145052,c_776]) ).

tcf(c_154911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145052,c_762]) ).

tcf(c_154912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145052,c_761]) ).

tcf(c_154913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145052,c_642]) ).

tcf(c_154914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145052,c_774]) ).

tcf(c_154915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145052,c_770]) ).

tcf(c_154916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145052,c_768]) ).

tcf(c_154917,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145052,c_763]) ).

tcf(c_155016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145053,c_144852]) ).

tcf(c_155017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145053,c_125973]) ).

tcf(c_155018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145053,c_125887]) ).

tcf(c_155019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_793]) ).

tcf(c_155020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145053,c_632]) ).

tcf(c_155021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145053,c_631]) ).

tcf(c_155022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_847]) ).

tcf(c_155023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145053,c_799]) ).

tcf(c_155024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_798]) ).

tcf(c_155025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145053,c_795]) ).

tcf(c_155026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_849]) ).

tcf(c_155027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_848]) ).

tcf(c_155029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_781]) ).

tcf(c_155030,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145053,c_794]) ).

tcf(c_155031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145053,c_784]) ).

tcf(c_155032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145053,c_800]) ).

tcf(c_155033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145053,c_786]) ).

tcf(c_155034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145053,c_789]) ).

tcf(c_155036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145053,c_806]) ).

tcf(c_155037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145053,c_633]) ).

tcf(c_155038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145053,c_776]) ).

tcf(c_155039,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145053,c_762]) ).

tcf(c_155040,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145053,c_761]) ).

tcf(c_155041,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145053,c_642]) ).

tcf(c_155042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145053,c_774]) ).

tcf(c_155043,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145053,c_770]) ).

tcf(c_155044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145053,c_768]) ).

tcf(c_155045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145053,c_763]) ).

tcf(c_155171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145054,c_144852]) ).

tcf(c_155172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145054,c_125973]) ).

tcf(c_155173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_145054,c_125887]) ).

tcf(c_155174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_793]) ).

tcf(c_155175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145054,c_632]) ).

tcf(c_155176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145054,c_631]) ).

tcf(c_155177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_847]) ).

tcf(c_155178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145054,c_799]) ).

tcf(c_155179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_798]) ).

tcf(c_155180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145054,c_795]) ).

tcf(c_155181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_849]) ).

tcf(c_155182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_848]) ).

tcf(c_155184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X1,X5,X2,X2)),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_781]) ).

tcf(c_155185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145054,c_794]) ).

tcf(c_155186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5))) ),
    inference(superposition,[status(thm)],[c_145054,c_784]) ).

tcf(c_155187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X4,X1,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145054,c_800]) ).

tcf(c_155188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X1,X4,X5,X5)),X6),X7),X8),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145054,c_786]) ).

tcf(c_155189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145054,c_789]) ).

tcf(c_155191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X2,X3),c_Pair(X0,X1,X4,X4)),X5),X6),X7),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145054,c_806]) ).

tcf(c_155192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145054,c_633]) ).

tcf(c_155193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_145054,c_776]) ).

tcf(c_155194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145054,c_762]) ).

tcf(c_155195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_145054,c_761]) ).

tcf(c_155196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145054,c_642]) ).

tcf(c_155197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145054,c_774]) ).

tcf(c_155198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_145054,c_770]) ).

tcf(c_155199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_145054,c_768]) ).

tcf(c_155200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_145054,c_763]) ).

tcf(c_155396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145055,c_144852]) ).

tcf(c_155397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145055,c_125973]) ).

tcf(c_155398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145055,c_125887]) ).

tcf(c_155399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_793]) ).

tcf(c_155400,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145055,c_632]) ).

tcf(c_155401,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145055,c_631]) ).

tcf(c_155402,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_847]) ).

tcf(c_155403,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145055,c_799]) ).

tcf(c_155404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_798]) ).

tcf(c_155405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145055,c_795]) ).

tcf(c_155406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_849]) ).

tcf(c_155407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_848]) ).

tcf(c_155409,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_781]) ).

tcf(c_155410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145055,c_794]) ).

tcf(c_155411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145055,c_784]) ).

tcf(c_155412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145055,c_800]) ).

tcf(c_155413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145055,c_786]) ).

tcf(c_155414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145055,c_789]) ).

tcf(c_155416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145055,c_806]) ).

tcf(c_155417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145055,c_633]) ).

tcf(c_155418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145055,c_776]) ).

tcf(c_155419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145055,c_762]) ).

tcf(c_155420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145055,c_761]) ).

tcf(c_155421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145055,c_642]) ).

tcf(c_155422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145055,c_774]) ).

tcf(c_155423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145055,c_770]) ).

tcf(c_155424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145055,c_768]) ).

tcf(c_155425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145055,c_763]) ).

tcf(c_155500,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145056,c_144852]) ).

tcf(c_155501,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145056,c_125973]) ).

tcf(c_155502,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145056,c_125887]) ).

tcf(c_155503,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_793]) ).

tcf(c_155504,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145056,c_632]) ).

tcf(c_155505,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145056,c_631]) ).

tcf(c_155506,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_847]) ).

tcf(c_155507,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145056,c_799]) ).

tcf(c_155508,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_798]) ).

tcf(c_155509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145056,c_795]) ).

tcf(c_155510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_849]) ).

tcf(c_155511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_848]) ).

tcf(c_155513,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_781]) ).

tcf(c_155514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145056,c_794]) ).

tcf(c_155515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145056,c_784]) ).

tcf(c_155516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145056,c_800]) ).

tcf(c_155517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145056,c_786]) ).

tcf(c_155518,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145056,c_789]) ).

tcf(c_155520,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145056,c_806]) ).

tcf(c_155521,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145056,c_633]) ).

tcf(c_155522,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145056,c_776]) ).

tcf(c_155523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145056,c_762]) ).

tcf(c_155524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145056,c_761]) ).

tcf(c_155525,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145056,c_642]) ).

tcf(c_155526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145056,c_774]) ).

tcf(c_155527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145056,c_770]) ).

tcf(c_155528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145056,c_768]) ).

tcf(c_155529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145056,c_763]) ).

tcf(c_155674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145057,c_144852]) ).

tcf(c_155675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145057,c_125973]) ).

tcf(c_155676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145057,c_125887]) ).

tcf(c_155677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_793]) ).

tcf(c_155678,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145057,c_632]) ).

tcf(c_155679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145057,c_631]) ).

tcf(c_155680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_847]) ).

tcf(c_155681,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145057,c_799]) ).

tcf(c_155682,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_798]) ).

tcf(c_155683,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145057,c_795]) ).

tcf(c_155684,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_849]) ).

tcf(c_155685,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_848]) ).

tcf(c_155687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_781]) ).

tcf(c_155688,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145057,c_794]) ).

tcf(c_155689,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145057,c_784]) ).

tcf(c_155690,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145057,c_800]) ).

tcf(c_155691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145057,c_786]) ).

tcf(c_155692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145057,c_789]) ).

tcf(c_155694,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145057,c_806]) ).

tcf(c_155695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145057,c_633]) ).

tcf(c_155696,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145057,c_776]) ).

tcf(c_155697,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145057,c_762]) ).

tcf(c_155698,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145057,c_761]) ).

tcf(c_155699,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145057,c_642]) ).

tcf(c_155700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145057,c_774]) ).

tcf(c_155701,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145057,c_770]) ).

tcf(c_155702,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145057,c_768]) ).

tcf(c_155703,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145057,c_763]) ).

tcf(c_155913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145058,c_144852]) ).

tcf(c_155914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145058,c_125973]) ).

tcf(c_155915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145058,c_125887]) ).

tcf(c_155916,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_793]) ).

tcf(c_155917,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145058,c_632]) ).

tcf(c_155918,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145058,c_631]) ).

tcf(c_155919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_847]) ).

tcf(c_155920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145058,c_799]) ).

tcf(c_155921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_798]) ).

tcf(c_155922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145058,c_795]) ).

tcf(c_155923,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_849]) ).

tcf(c_155924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_848]) ).

tcf(c_155926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_781]) ).

tcf(c_155927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145058,c_794]) ).

tcf(c_155928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145058,c_784]) ).

tcf(c_155929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145058,c_800]) ).

tcf(c_155930,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145058,c_786]) ).

tcf(c_155931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145058,c_789]) ).

tcf(c_155933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145058,c_806]) ).

tcf(c_155934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145058,c_633]) ).

tcf(c_155935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145058,c_776]) ).

tcf(c_155936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145058,c_762]) ).

tcf(c_155937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145058,c_761]) ).

tcf(c_155938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145058,c_642]) ).

tcf(c_155939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145058,c_774]) ).

tcf(c_155940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145058,c_770]) ).

tcf(c_155941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145058,c_768]) ).

tcf(c_155942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145058,c_763]) ).

tcf(c_156147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145064,c_144852]) ).

tcf(c_156148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145064,c_125973]) ).

tcf(c_156149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145064,c_125887]) ).

tcf(c_156150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_793]) ).

tcf(c_156151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145064,c_632]) ).

tcf(c_156152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145064,c_631]) ).

tcf(c_156153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_847]) ).

tcf(c_156154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145064,c_799]) ).

tcf(c_156155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_798]) ).

tcf(c_156156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145064,c_795]) ).

tcf(c_156157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_849]) ).

tcf(c_156158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_848]) ).

tcf(c_156160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_781]) ).

tcf(c_156161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145064,c_794]) ).

tcf(c_156162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145064,c_784]) ).

tcf(c_156163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145064,c_800]) ).

tcf(c_156164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145064,c_786]) ).

tcf(c_156165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145064,c_789]) ).

tcf(c_156167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145064,c_806]) ).

tcf(c_156168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145064,c_633]) ).

tcf(c_156169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145064,c_776]) ).

tcf(c_156170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145064,c_762]) ).

tcf(c_156171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145064,c_761]) ).

tcf(c_156172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145064,c_642]) ).

tcf(c_156173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145064,c_774]) ).

tcf(c_156174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145064,c_770]) ).

tcf(c_156175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145064,c_768]) ).

tcf(c_156176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145064,c_763]) ).

tcf(c_156419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145071,c_144852]) ).

tcf(c_156420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145071,c_125973]) ).

tcf(c_156421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145071,c_125887]) ).

tcf(c_156422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_793]) ).

tcf(c_156423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145071,c_632]) ).

tcf(c_156424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145071,c_631]) ).

tcf(c_156425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_847]) ).

tcf(c_156426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145071,c_799]) ).

tcf(c_156427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_798]) ).

tcf(c_156428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145071,c_795]) ).

tcf(c_156429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_849]) ).

tcf(c_156430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_848]) ).

tcf(c_156432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_781]) ).

tcf(c_156433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145071,c_794]) ).

tcf(c_156434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145071,c_784]) ).

tcf(c_156435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145071,c_800]) ).

tcf(c_156436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145071,c_786]) ).

tcf(c_156437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145071,c_789]) ).

tcf(c_156439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145071,c_806]) ).

tcf(c_156440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145071,c_633]) ).

tcf(c_156441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145071,c_776]) ).

tcf(c_156442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145071,c_762]) ).

tcf(c_156443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145071,c_761]) ).

tcf(c_156444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145071,c_642]) ).

tcf(c_156445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145071,c_774]) ).

tcf(c_156446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145071,c_770]) ).

tcf(c_156447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145071,c_768]) ).

tcf(c_156448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145071,c_763]) ).

tcf(c_156564,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145078,c_144852]) ).

tcf(c_156565,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145078,c_125973]) ).

tcf(c_156566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145078,c_125887]) ).

tcf(c_156567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_793]) ).

tcf(c_156568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145078,c_632]) ).

tcf(c_156569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145078,c_631]) ).

tcf(c_156570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_847]) ).

tcf(c_156571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145078,c_799]) ).

tcf(c_156572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_798]) ).

tcf(c_156573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145078,c_795]) ).

tcf(c_156574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_849]) ).

tcf(c_156575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_848]) ).

tcf(c_156577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_781]) ).

tcf(c_156578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145078,c_794]) ).

tcf(c_156579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145078,c_784]) ).

tcf(c_156580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145078,c_800]) ).

tcf(c_156581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145078,c_786]) ).

tcf(c_156582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145078,c_789]) ).

tcf(c_156584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145078,c_806]) ).

tcf(c_156585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145078,c_633]) ).

tcf(c_156586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145078,c_776]) ).

tcf(c_156587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145078,c_762]) ).

tcf(c_156588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145078,c_761]) ).

tcf(c_156589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145078,c_642]) ).

tcf(c_156590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145078,c_774]) ).

tcf(c_156591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145078,c_770]) ).

tcf(c_156592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145078,c_768]) ).

tcf(c_156593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145078,c_763]) ).

tcf(c_156720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_834,c_7263,c_7265]) ).

tcf(c_156755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156720,c_768]) ).

tcf(c_156758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OCond(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156720,c_136744]) ).

tcf(c_156785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_836,c_7263,c_7265]) ).

tcf(c_156820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156785,c_768]) ).

tcf(c_156823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAcc(X2,X5,X6,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156785,c_136744]) ).

tcf(c_156850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_654,c_7263,c_7265]) ).

tcf(c_156885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156850,c_768]) ).

tcf(c_156888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156850,c_136744]) ).

tcf(c_156915,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_657,c_7263,c_7265]) ).

tcf(c_156950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156915,c_768]) ).

tcf(c_156953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCond(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_156915,c_136744]) ).

tcf(c_156983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145079,c_144852]) ).

tcf(c_156984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145079,c_125973]) ).

tcf(c_156985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145079,c_125887]) ).

tcf(c_156986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_793]) ).

tcf(c_156987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145079,c_632]) ).

tcf(c_156988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145079,c_631]) ).

tcf(c_156989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_847]) ).

tcf(c_156990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145079,c_799]) ).

tcf(c_156991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_798]) ).

tcf(c_156992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145079,c_795]) ).

tcf(c_156993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_849]) ).

tcf(c_156994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_848]) ).

tcf(c_156996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_781]) ).

tcf(c_156997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145079,c_794]) ).

tcf(c_156998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145079,c_784]) ).

tcf(c_156999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145079,c_800]) ).

tcf(c_157000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145079,c_786]) ).

tcf(c_157001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145079,c_789]) ).

tcf(c_157003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145079,c_806]) ).

tcf(c_157004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145079,c_633]) ).

tcf(c_157005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145079,c_776]) ).

tcf(c_157006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145079,c_762]) ).

tcf(c_157007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145079,c_761]) ).

tcf(c_157008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145079,c_642]) ).

tcf(c_157009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145079,c_774]) ).

tcf(c_157010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145079,c_770]) ).

tcf(c_157011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145079,c_768]) ).

tcf(c_157012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145079,c_763]) ).

tcf(c_157145,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145080,c_144852]) ).

tcf(c_157146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145080,c_125973]) ).

tcf(c_157147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145080,c_125887]) ).

tcf(c_157148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_793]) ).

tcf(c_157149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145080,c_632]) ).

tcf(c_157150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145080,c_631]) ).

tcf(c_157151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_847]) ).

tcf(c_157152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145080,c_799]) ).

tcf(c_157153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_798]) ).

tcf(c_157154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145080,c_795]) ).

tcf(c_157155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_849]) ).

tcf(c_157156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_848]) ).

tcf(c_157158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_781]) ).

tcf(c_157159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145080,c_794]) ).

tcf(c_157160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145080,c_784]) ).

tcf(c_157161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145080,c_800]) ).

tcf(c_157162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145080,c_786]) ).

tcf(c_157163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145080,c_789]) ).

tcf(c_157165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145080,c_806]) ).

tcf(c_157166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145080,c_633]) ).

tcf(c_157167,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145080,c_776]) ).

tcf(c_157168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145080,c_762]) ).

tcf(c_157169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145080,c_761]) ).

tcf(c_157170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145080,c_642]) ).

tcf(c_157171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145080,c_774]) ).

tcf(c_157172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145080,c_770]) ).

tcf(c_157173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145080,c_768]) ).

tcf(c_157174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145080,c_763]) ).

tcf(c_157275,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145081,c_144852]) ).

tcf(c_157276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145081,c_125973]) ).

tcf(c_157277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145081,c_125887]) ).

tcf(c_157278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_793]) ).

tcf(c_157279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145081,c_632]) ).

tcf(c_157280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145081,c_631]) ).

tcf(c_157281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_847]) ).

tcf(c_157282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145081,c_799]) ).

tcf(c_157283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_798]) ).

tcf(c_157284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145081,c_795]) ).

tcf(c_157285,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_849]) ).

tcf(c_157286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_848]) ).

tcf(c_157288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_781]) ).

tcf(c_157289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145081,c_794]) ).

tcf(c_157290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145081,c_784]) ).

tcf(c_157291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145081,c_800]) ).

tcf(c_157292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145081,c_786]) ).

tcf(c_157293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145081,c_789]) ).

tcf(c_157295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145081,c_806]) ).

tcf(c_157296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145081,c_633]) ).

tcf(c_157297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145081,c_776]) ).

tcf(c_157298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145081,c_762]) ).

tcf(c_157299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145081,c_761]) ).

tcf(c_157300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145081,c_642]) ).

tcf(c_157301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145081,c_774]) ).

tcf(c_157302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145081,c_770]) ).

tcf(c_157303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145081,c_768]) ).

tcf(c_157304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145081,c_763]) ).

tcf(c_157451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145082,c_144852]) ).

tcf(c_157452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145082,c_125973]) ).

tcf(c_157453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145082,c_125887]) ).

tcf(c_157454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_793]) ).

tcf(c_157455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145082,c_632]) ).

tcf(c_157456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145082,c_631]) ).

tcf(c_157457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_847]) ).

tcf(c_157458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145082,c_799]) ).

tcf(c_157459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_798]) ).

tcf(c_157460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145082,c_795]) ).

tcf(c_157461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_849]) ).

tcf(c_157462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_848]) ).

tcf(c_157464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_781]) ).

tcf(c_157465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145082,c_794]) ).

tcf(c_157466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145082,c_784]) ).

tcf(c_157467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145082,c_800]) ).

tcf(c_157468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145082,c_786]) ).

tcf(c_157469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145082,c_789]) ).

tcf(c_157471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145082,c_806]) ).

tcf(c_157472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145082,c_633]) ).

tcf(c_157473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145082,c_776]) ).

tcf(c_157474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145082,c_762]) ).

tcf(c_157475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145082,c_761]) ).

tcf(c_157476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145082,c_642]) ).

tcf(c_157477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145082,c_774]) ).

tcf(c_157478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145082,c_770]) ).

tcf(c_157479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145082,c_768]) ).

tcf(c_157480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145082,c_763]) ).

tcf(c_157601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145083,c_144852]) ).

tcf(c_157602,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145083,c_125973]) ).

tcf(c_157603,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_145083,c_125887]) ).

tcf(c_157604,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_793]) ).

tcf(c_157605,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145083,c_632]) ).

tcf(c_157606,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145083,c_631]) ).

tcf(c_157607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_847]) ).

tcf(c_157608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145083,c_799]) ).

tcf(c_157609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_798]) ).

tcf(c_157610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),X3,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145083,c_795]) ).

tcf(c_157611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_849]) ).

tcf(c_157612,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_848]) ).

tcf(c_157614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X3,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X3,X2,X2)),X4),X5),X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_781]) ).

tcf(c_157615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145083,c_794]) ).

tcf(c_157616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3))) ),
    inference(superposition,[status(thm)],[c_145083,c_784]) ).

tcf(c_157617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X2,X1,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145083,c_800]) ).

tcf(c_157618,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145083,c_786]) ).

tcf(c_157619,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145083,c_789]) ).

tcf(c_157621,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2,X2),X2)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145083,c_806]) ).

tcf(c_157622,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145083,c_633]) ).

tcf(c_157623,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_145083,c_776]) ).

tcf(c_157624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145083,c_762]) ).

tcf(c_157625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_145083,c_761]) ).

tcf(c_157626,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145083,c_642]) ).

tcf(c_157627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145083,c_774]) ).

tcf(c_157628,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_145083,c_770]) ).

tcf(c_157629,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_145083,c_768]) ).

tcf(c_157630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145083,c_763]) ).

tcf(c_157861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145089,c_562]) ).

tcf(c_157862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145089,c_561]) ).

tcf(c_157863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145089,c_565]) ).

tcf(c_157864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145089,c_144852]) ).

tcf(c_157865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145089,c_125973]) ).

tcf(c_157866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145089,c_125887]) ).

tcf(c_157868,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),X7,X7),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145089,c_632]) ).

tcf(c_157869,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),X7,X7),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145089,c_631]) ).

tcf(c_157872,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145089,c_798]) ).

tcf(c_157877,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145089,c_781]) ).

tcf(c_157878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7))) ),
    inference(superposition,[status(thm)],[c_145089,c_794]) ).

tcf(c_157879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7))) ),
    inference(superposition,[status(thm)],[c_145089,c_784]) ).

tcf(c_157880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145089,c_800]) ).

tcf(c_157881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145089,c_786]) ).

tcf(c_157884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7,X7),X7)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145089,c_806]) ).

tcf(c_157885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145089,c_633]) ).

tcf(c_157886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145089,c_776]) ).

tcf(c_157887,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_145089,c_762]) ).

tcf(c_157889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145089,c_642]) ).

tcf(c_157890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145089,c_774]) ).

tcf(c_157891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_145089,c_770]) ).

tcf(c_157892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_145089,c_768]) ).

tcf(c_157893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145089,c_763]) ).

tcf(c_157929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_157889,c_145089]) ).

tcf(c_157934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_157885,c_145089]) ).

tcf(c_157960,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145090,c_562]) ).

tcf(c_157961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145090,c_561]) ).

tcf(c_157962,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145090,c_565]) ).

tcf(c_157963,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145090,c_144852]) ).

tcf(c_157964,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145090,c_125973]) ).

tcf(c_157965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145090,c_125887]) ).

tcf(c_157967,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),X7,X7),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145090,c_632]) ).

tcf(c_157968,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7),X7,X7),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145090,c_631]) ).

tcf(c_157971,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145090,c_798]) ).

tcf(c_157976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145090,c_781]) ).

tcf(c_157977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7))) ),
    inference(superposition,[status(thm)],[c_145090,c_794]) ).

tcf(c_157978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7))) ),
    inference(superposition,[status(thm)],[c_145090,c_784]) ).

tcf(c_157979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145090,c_800]) ).

tcf(c_157980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145090,c_786]) ).

tcf(c_157983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4,X5),X6),X7,X7),X7)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145090,c_806]) ).

tcf(c_157984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145090,c_633]) ).

tcf(c_157985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145090,c_776]) ).

tcf(c_157986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_145090,c_762]) ).

tcf(c_157988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145090,c_642]) ).

tcf(c_157989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145090,c_774]) ).

tcf(c_157990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_145090,c_770]) ).

tcf(c_157991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_145090,c_768]) ).

tcf(c_157992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145090,c_763]) ).

tcf(c_158028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_157988,c_145090]) ).

tcf(c_158033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_157984,c_145090]) ).

tcf(c_158073,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X3,X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145093,c_144852]) ).

tcf(c_158074,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_145093,c_125973]) ).

tcf(c_158075,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_145093,c_125887]) ).

tcf(c_158076,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X0,X4,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X0,X4,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X0,X4,X2,X2),X5,X6,X7)),X6,X7),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X0,X4,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_793]) ).

tcf(c_158077,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),X4),X4,X4),c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145093,c_632]) ).

tcf(c_158078,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),X4),X4,X4),c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145093,c_631]) ).

tcf(c_158079,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_847]) ).

tcf(c_158080,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145093,c_799]) ).

tcf(c_158081,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_798]) ).

tcf(c_158082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145093,c_795]) ).

tcf(c_158083,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_849]) ).

tcf(c_158084,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X1,X4,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X1,X4,X2,X2),X5,X6,X7)),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_848]) ).

tcf(c_158086,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X1,X4,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X1,X4,X2,X2),X5,X6,X7)),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_781]) ).

tcf(c_158087,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),X4))) ),
    inference(superposition,[status(thm)],[c_145093,c_794]) ).

tcf(c_158088,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),X4))) ),
    inference(superposition,[status(thm)],[c_145093,c_784]) ).

tcf(c_158089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X3,X1,X4,X4),X5,X6,X7)),X6,X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145093,c_800]) ).

tcf(c_158090,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X1,X3,X4,X4),X5,X6,X7)),X6,X7),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145093,c_786]) ).

tcf(c_158091,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X0,X1,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145093,c_789]) ).

tcf(c_158093,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(hAPP(c_fequal(X2),c_Pair(c_Pair(X0,X1,X3,X3),X4,X5,X6)),X5,X6),X3,X3),X3)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145093,c_806]) ).

tcf(c_158094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145093,c_633]) ).

tcf(c_158095,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X5,X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X5,X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_145093,c_776]) ).

tcf(c_158096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X6,X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_145093,c_762]) ).

tcf(c_158097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X6,X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_145093,c_761]) ).

tcf(c_158098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145093,c_642]) ).

tcf(c_158099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,X7,X8)),X7,X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145093,c_774]) ).

tcf(c_158100,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,X6,X7)),X6,X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_145093,c_770]) ).

tcf(c_158101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,X6,X7)),X6,X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_145093,c_768]) ).

tcf(c_158102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145093,c_763]) ).

tcf(c_158209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145094,c_562]) ).

tcf(c_158210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145094,c_561]) ).

tcf(c_158211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145094,c_565]) ).

tcf(c_158212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145094,c_144852]) ).

tcf(c_158213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145094,c_125973]) ).

tcf(c_158214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145094,c_125887]) ).

tcf(c_158216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145094,c_632]) ).

tcf(c_158217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145094,c_631]) ).

tcf(c_158220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145094,c_798]) ).

tcf(c_158225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145094,c_781]) ).

tcf(c_158226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145094,c_794]) ).

tcf(c_158227,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145094,c_784]) ).

tcf(c_158228,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145094,c_800]) ).

tcf(c_158229,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145094,c_786]) ).

tcf(c_158232,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7,X7),X7)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145094,c_806]) ).

tcf(c_158233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145094,c_633]) ).

tcf(c_158234,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145094,c_776]) ).

tcf(c_158235,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_145094,c_762]) ).

tcf(c_158237,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145094,c_642]) ).

tcf(c_158238,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145094,c_774]) ).

tcf(c_158239,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_145094,c_770]) ).

tcf(c_158240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_145094,c_768]) ).

tcf(c_158241,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145094,c_763]) ).

tcf(c_158277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_158237,c_145094]) ).

tcf(c_158282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_158233,c_145094]) ).

tcf(c_158356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X3),X4),X5),
    inference(superposition,[status(thm)],[c_743,c_145095]) ).

tcf(c_158361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145095,c_562]) ).

tcf(c_158362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145095,c_561]) ).

tcf(c_158363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145095,c_565]) ).

tcf(c_158364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145095,c_144852]) ).

tcf(c_158365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145095,c_125973]) ).

tcf(c_158366,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145095,c_125887]) ).

tcf(c_158368,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145095,c_632]) ).

tcf(c_158369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145095,c_631]) ).

tcf(c_158372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145095,c_798]) ).

tcf(c_158377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145095,c_781]) ).

tcf(c_158378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145095,c_794]) ).

tcf(c_158379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145095,c_784]) ).

tcf(c_158380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145095,c_800]) ).

tcf(c_158381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145095,c_786]) ).

tcf(c_158384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X2,X3),X3,X3),X4),X5,X6),X7,X7),X7)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145095,c_806]) ).

tcf(c_158385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145095,c_633]) ).

tcf(c_158386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145095,c_776]) ).

tcf(c_158387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_145095,c_762]) ).

tcf(c_158389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145095,c_642]) ).

tcf(c_158390,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145095,c_774]) ).

tcf(c_158391,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_145095,c_770]) ).

tcf(c_158392,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_145095,c_768]) ).

tcf(c_158393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145095,c_763]) ).

tcf(c_158429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_158389,c_145095]) ).

tcf(c_158434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_158385,c_145095]) ).

tcf(c_158446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145096,c_562]) ).

tcf(c_158447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145096,c_561]) ).

tcf(c_158448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145096,c_565]) ).

tcf(c_158449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145096,c_144852]) ).

tcf(c_158450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145096,c_125973]) ).

tcf(c_158451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145096,c_125887]) ).

tcf(c_158453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145096,c_632]) ).

tcf(c_158454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145096,c_631]) ).

tcf(c_158457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145096,c_798]) ).

tcf(c_158462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145096,c_781]) ).

tcf(c_158463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145096,c_794]) ).

tcf(c_158464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145096,c_784]) ).

tcf(c_158465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145096,c_800]) ).

tcf(c_158466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145096,c_786]) ).

tcf(c_158469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7,X7),X7)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145096,c_806]) ).

tcf(c_158470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145096,c_633]) ).

tcf(c_158471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145096,c_776]) ).

tcf(c_158472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_145096,c_762]) ).

tcf(c_158474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145096,c_642]) ).

tcf(c_158475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145096,c_774]) ).

tcf(c_158476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_145096,c_770]) ).

tcf(c_158477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_145096,c_768]) ).

tcf(c_158478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145096,c_763]) ).

tcf(c_158514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_158474,c_145096]) ).

tcf(c_158519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_158470,c_145096]) ).

tcf(c_158569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145097,c_562]) ).

tcf(c_158570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145097,c_561]) ).

tcf(c_158571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145097,c_565]) ).

tcf(c_158572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_145097,c_144852]) ).

tcf(c_158573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145097,c_125973]) ).

tcf(c_158574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_145097,c_125887]) ).

tcf(c_158576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145097,c_632]) ).

tcf(c_158577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7),X7,X7),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),tc_prod(X7,X7))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145097,c_631]) ).

tcf(c_158580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145097,c_798]) ).

tcf(c_158585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145097,c_781]) ).

tcf(c_158586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145097,c_794]) ).

tcf(c_158587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7))) ),
    inference(superposition,[status(thm)],[c_145097,c_784]) ).

tcf(c_158588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145097,c_800]) ).

tcf(c_158589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X0,X8))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145097,c_786]) ).

tcf(c_158592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X5,X6),X7,X7),X7)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145097,c_806]) ).

tcf(c_158593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145097,c_633]) ).

tcf(c_158594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_145097,c_776]) ).

tcf(c_158595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_145097,c_762]) ).

tcf(c_158597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145097,c_642]) ).

tcf(c_158598,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145097,c_774]) ).

tcf(c_158599,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_145097,c_770]) ).

tcf(c_158600,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_145097,c_768]) ).

tcf(c_158601,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_145097,c_763]) ).

tcf(c_158637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_158597,c_145097]) ).

tcf(c_158642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_158593,c_145097]) ).

tcf(c_158724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_756,c_7263,c_7265]) ).

tcf(c_158759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158724,c_768]) ).

tcf(c_158762,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OCall(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158724,c_136744]) ).

tcf(c_158789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_758,c_7263,c_7265]) ).

tcf(c_158824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158789,c_768]) ).

tcf(c_158827,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAcc(X0,X5,X6,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158789,c_136744]) ).

tcf(c_158854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_583,c_7263,c_7265]) ).

tcf(c_158889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158854,c_768]) ).

tcf(c_158892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158854,c_136744]) ).

tcf(c_158919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_759,c_7263,c_7265]) ).

tcf(c_158954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158919,c_768]) ).

tcf(c_158957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_158919,c_136744]) ).

tcf(c_158984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_687,c_145099]) ).

tcf(c_158985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_698,c_145099]) ).

tcf(c_158990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145099,c_562]) ).

tcf(c_158991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145099,c_561]) ).

tcf(c_158992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145099,c_565]) ).

tcf(c_158993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_145099,c_144852]) ).

tcf(c_158994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_145099,c_125973]) ).

tcf(c_158995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_145099,c_125887]) ).

tcf(c_158997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145099,c_632]) ).

tcf(c_158998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145099,c_631]) ).

tcf(c_159001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145099,c_798]) ).

tcf(c_159006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145099,c_781]) ).

tcf(c_159007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_145099,c_794]) ).

tcf(c_159008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_145099,c_784]) ).

tcf(c_159009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145099,c_800]) ).

tcf(c_159010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145099,c_786]) ).

tcf(c_159013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145099,c_806]) ).

tcf(c_159014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145099,c_633]) ).

tcf(c_159015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145099,c_776]) ).

tcf(c_159016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_145099,c_762]) ).

tcf(c_159018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145099,c_642]) ).

tcf(c_159019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145099,c_774]) ).

tcf(c_159020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_145099,c_770]) ).

tcf(c_159021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_145099,c_768]) ).

tcf(c_159022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_145099,c_763]) ).

tcf(c_159058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_159018,c_145099]) ).

tcf(c_159063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_159014,c_145099]) ).

tcf(c_159082,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X3),X4),
    inference(demodulation,[status(thm)],[c_158985,c_596]) ).

tcf(c_159083,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_596,c_145100]) ).

tcf(c_159089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145100,c_562]) ).

tcf(c_159090,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145100,c_561]) ).

tcf(c_159091,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145100,c_565]) ).

tcf(c_159092,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_145100,c_144852]) ).

tcf(c_159093,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_145100,c_125973]) ).

tcf(c_159094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_145100,c_125887]) ).

tcf(c_159096,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145100,c_632]) ).

tcf(c_159097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5),X5,X5),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145100,c_631]) ).

tcf(c_159100,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145100,c_798]) ).

tcf(c_159105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145100,c_781]) ).

tcf(c_159106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_145100,c_794]) ).

tcf(c_159107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5))) ),
    inference(superposition,[status(thm)],[c_145100,c_784]) ).

tcf(c_159108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145100,c_800]) ).

tcf(c_159109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145100,c_786]) ).

tcf(c_159112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X3),X4),X3,X3),X3,X3),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145100,c_806]) ).

tcf(c_159113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145100,c_633]) ).

tcf(c_159114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145100,c_776]) ).

tcf(c_159115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_145100,c_762]) ).

tcf(c_159117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145100,c_642]) ).

tcf(c_159118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145100,c_774]) ).

tcf(c_159119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_145100,c_770]) ).

tcf(c_159120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_145100,c_768]) ).

tcf(c_159121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_145100,c_763]) ).

tcf(c_159157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_159117,c_145100]) ).

tcf(c_159162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_159113,c_145100]) ).

tcf(c_159192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145135,c_560]) ).

tcf(c_159193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145135,c_564]) ).

tcf(c_159194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145135,c_562]) ).

tcf(c_159195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145135,c_561]) ).

tcf(c_159196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X6))
      | hBOOL(hAPP(X7,X0))
      | c_in(c_Pair(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X7,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5,X5),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145135,c_565]) ).

tcf(c_159197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_145135,c_144852]) ).

tcf(c_159198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_145135,c_125973]) ).

tcf(c_159199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_145135,c_125887]) ).

tcf(c_159200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_793]) ).

tcf(c_159201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145135,c_632]) ).

tcf(c_159202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145135,c_631]) ).

tcf(c_159203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_847]) ).

tcf(c_159204,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145135,c_799]) ).

tcf(c_159205,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_798]) ).

tcf(c_159206,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145135,c_795]) ).

tcf(c_159207,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_849]) ).

tcf(c_159208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X6,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_848]) ).

tcf(c_159210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X6,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_781]) ).

tcf(c_159211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_145135,c_794]) ).

tcf(c_159212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_145135,c_784]) ).

tcf(c_159213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145135,c_800]) ).

tcf(c_159214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145135,c_786]) ).

tcf(c_159215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145135,c_789]) ).

tcf(c_159217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X5,X5),X2,X3)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145135,c_806]) ).

tcf(c_159218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145135,c_633]) ).

tcf(c_159219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X5,X5),X1,X2)
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145135,c_776]) ).

tcf(c_159220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_145135,c_762]) ).

tcf(c_159221,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X6,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_145135,c_761]) ).

tcf(c_159222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X3),X4,X5)
      | ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145135,c_642]) ).

tcf(c_159223,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X3,X2,X8),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145135,c_774]) ).

tcf(c_159224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X6,X5),X6) ),
    inference(superposition,[status(thm)],[c_145135,c_770]) ).

tcf(c_159225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X5) ),
    inference(superposition,[status(thm)],[c_145135,c_768]) ).

tcf(c_159226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X1)
      | c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_145135,c_763]) ).

tcf(c_159461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145136,c_560]) ).

tcf(c_159462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145136,c_564]) ).

tcf(c_159463,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145136,c_562]) ).

tcf(c_159464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145136,c_561]) ).

tcf(c_159465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X6))
      | hBOOL(hAPP(X7,X0))
      | c_in(c_Pair(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X7,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5,X5),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145136,c_565]) ).

tcf(c_159466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_145136,c_144852]) ).

tcf(c_159467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_145136,c_125973]) ).

tcf(c_159468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_145136,c_125887]) ).

tcf(c_159469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_793]) ).

tcf(c_159470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145136,c_632]) ).

tcf(c_159471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145136,c_631]) ).

tcf(c_159472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_847]) ).

tcf(c_159473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145136,c_799]) ).

tcf(c_159474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_798]) ).

tcf(c_159475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145136,c_795]) ).

tcf(c_159476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_849]) ).

tcf(c_159477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X6,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_848]) ).

tcf(c_159479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X1,X6,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_781]) ).

tcf(c_159480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_145136,c_794]) ).

tcf(c_159481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_145136,c_784]) ).

tcf(c_159482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X1,X5,X5),X2,X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145136,c_800]) ).

tcf(c_159483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X1,X6,X5,X5),X2,X3)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_145136,c_786]) ).

tcf(c_159484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145136,c_789]) ).

tcf(c_159486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X5,X5),X2,X3)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_145136,c_806]) ).

tcf(c_159487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145136,c_633]) ).

tcf(c_159488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X5,X5),X1,X2)
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_145136,c_776]) ).

tcf(c_159489,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_145136,c_762]) ).

tcf(c_159490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X6,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_145136,c_761]) ).

tcf(c_159491,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X3),X4,X5)
      | ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_145136,c_642]) ).

tcf(c_159492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X3,X2,X8),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145136,c_774]) ).

tcf(c_159493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X6,X5),X6) ),
    inference(superposition,[status(thm)],[c_145136,c_770]) ).

tcf(c_159494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X5) ),
    inference(superposition,[status(thm)],[c_145136,c_768]) ).

tcf(c_159495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X1)
      | c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_145136,c_763]) ).

tcf(c_159639,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145859,c_560]) ).

tcf(c_159640,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145859,c_564]) ).

tcf(c_159641,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145859,c_562]) ).

tcf(c_159642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_145859,c_561]) ).

tcf(c_159643,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_145859,c_565]) ).

tcf(c_159644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_145859,c_144852]) ).

tcf(c_159645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145859,c_125973]) ).

tcf(c_159646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_145859,c_125887]) ).

tcf(c_159647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145859,c_633]) ).

tcf(c_159649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_145859,c_762]) ).

tcf(c_159651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145859,c_797]) ).

tcf(c_159655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_145859,c_796]) ).

tcf(c_159656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_145859,c_642]) ).

tcf(c_159657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_145859,c_774]) ).

tcf(c_159658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145859,c_770]) ).

tcf(c_159659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_145859,c_768]) ).

tcf(c_159660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_145859,c_763]) ).

tcf(c_159711,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_159659,c_562]) ).

tcf(c_159712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_159659,c_561]) ).

tcf(c_159713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_159659,c_565]) ).

tcf(c_159714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_159659,c_144852]) ).

tcf(c_159715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_159659,c_125973]) ).

tcf(c_159716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_159659,c_125887]) ).

tcf(c_159717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_159659,c_633]) ).

tcf(c_159718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_159659,c_776]) ).

tcf(c_159719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_159659,c_762]) ).

tcf(c_159721,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_159659,c_642]) ).

tcf(c_159722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_159659,c_774]) ).

tcf(c_159723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_159659,c_770]) ).

tcf(c_159724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_159659,c_768]) ).

tcf(c_159725,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_159659,c_763]) ).

tcf(c_159726,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_159659,c_840]) ).

tcf(c_159727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_159659,c_126501]) ).

tcf(c_159745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_159721,c_159659]) ).

tcf(c_159748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_159717,c_159659]) ).

tcf(c_159845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_159726,c_841]) ).

tcf(c_159852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_159845,c_562]) ).

tcf(c_159853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_159845,c_561]) ).

tcf(c_159854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_159845,c_565]) ).

tcf(c_159855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_159845,c_144852]) ).

tcf(c_159856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_159845,c_125973]) ).

tcf(c_159857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_159845,c_125887]) ).

tcf(c_159858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_159845,c_633]) ).

tcf(c_159859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_159845,c_776]) ).

tcf(c_159860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_159845,c_762]) ).

tcf(c_159862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_159845,c_642]) ).

tcf(c_159863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_159845,c_774]) ).

tcf(c_159864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_159845,c_770]) ).

tcf(c_159865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_159845,c_768]) ).

tcf(c_159866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_159845,c_763]) ).

tcf(c_159886,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_159862,c_159845]) ).

tcf(c_159889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_159858,c_159845]) ).

tcf(c_159950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X3)),X3,X3),X1)),
    inference(superposition,[status(thm)],[c_743,c_145873]) ).

tcf(c_159951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X3,X4),X6),
    inference(superposition,[status(thm)],[c_145873,c_841]) ).

tcf(c_159952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X3,X4),X6),
    inference(superposition,[status(thm)],[c_145901,c_841]) ).

tcf(c_159958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_145937,c_841]) ).

tcf(c_159959,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_829,c_7263,c_7265]) ).

tcf(c_159994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_159959,c_768]) ).

tcf(c_159997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OTryCatch(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OTryCatch(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_159959,c_136744]) ).

tcf(c_160024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_837,c_7263,c_7265]) ).

tcf(c_160059,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160024,c_768]) ).

tcf(c_160062,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X5,X6,X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(X2,X5,X6,X7,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160024,c_136744]) ).

tcf(c_160089,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_580,c_7263,c_7265]) ).

tcf(c_160124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160089,c_768]) ).

tcf(c_160127,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160089,c_136744]) ).

tcf(c_160154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_581,c_7263,c_7265]) ).

tcf(c_160189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160154,c_768]) ).

tcf(c_160192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160154,c_136744]) ).

tcf(c_160211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X3),X4)),
    inference(superposition,[status(thm)],[c_743,c_146521]) ).

tcf(c_160217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_146521,c_841]) ).

tcf(c_160223,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_146599,c_841]) ).

tcf(c_160224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X3),X4)),
    inference(superposition,[status(thm)],[c_743,c_146666]) ).

tcf(c_160229,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_146666,c_841]) ).

tcf(c_160234,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X0,X1),X2,X1))) ),
    inference(superposition,[status(thm)],[c_724,c_147143]) ).

tcf(c_160235,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1))) ),
    inference(superposition,[status(thm)],[c_743,c_147143]) ).

tcf(c_160236,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),c_Relation_ODomain(X0,X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_147143,c_841]) ).

tcf(c_160243,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_645,c_7263,c_7265]) ).

tcf(c_160250,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,c_Map_Omap__add(X8,X2,iPr_def_10,tc_Value_Oval),iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(c_Map_Omap__add(X7,X8,iPr_def_10,tc_Value_Oval),X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_675,c_160243]) ).

tcf(c_160251,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(c_Map_Omap__add(X7,X8,iPr_def_10,tc_Value_Oval),X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,c_Map_Omap__add(X8,X5,iPr_def_10,tc_Value_Oval),iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_675,c_160243]) ).

tcf(c_160252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_144852]) ).

tcf(c_160253,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_125973]) ).

tcf(c_160254,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_125887]) ).

tcf(c_160255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Otrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_633]) ).

tcf(c_160256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Wellfounded_Oacc(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_776]) ).

tcf(c_160257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X8,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X7,c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_762]) ).

tcf(c_160258,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X8,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X7,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_Relation_Orefl__on(X7,c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_761]) ).

tcf(c_160259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))) = X8 )
      | ~ c_Relation_Osingle__valued(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_642]) ).

tcf(c_160260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_OImage(c_SmallStep_Ored(X6),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_774]) ).

tcf(c_160261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Relation_Oconverse(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_770]) ).

tcf(c_160262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_768]) ).

tcf(c_160263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X8,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X8,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X8,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X8,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))),X7,tc_prod(tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_Relation_Orefl__on(c_SmallStep_Ored(X6),X7,tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_763]) ).

tcf(c_160264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(c_SmallStep_Ored(X6),c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_840]) ).

tcf(c_160265,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X6,X8,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X6,X8,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))
      | ~ c_WellTypeRT_OWTrt(X6,c_State_Ohp(c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),X8,X0,X9)
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_SmallStep_Ored(X6),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160243,c_149320]) ).

tcf(c_160338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_757,c_7263,c_7265]) ).

tcf(c_160375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160338,c_768]) ).

tcf(c_160378,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X0,c_Pair(X1,c_Map_Omap__add(X7,X2,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,c_Map_Omap__add(X7,X5,iPr_def_10,tc_Value_Oval),tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8)
      | ~ c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X6),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_160338,c_136744]) ).

tcf(c_160389,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X0,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X5,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_582,c_7263,c_7265]) ).

tcf(c_160399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(c_Expr_Oexp_OVal(X5,iPr_def_10),X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_125781,c_160389]) ).

tcf(c_160402,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X0,X8,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,iPr_def_10),X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X5,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,iPr_def_10),X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_584,c_7263,c_7265]) ).

tcf(c_160412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_125781,c_160402]) ).

tcf(c_160419,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X0,X1),X2,X1))) ),
    inference(superposition,[status(thm)],[c_724,c_147183]) ).

tcf(c_160420,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1))) ),
    inference(superposition,[status(thm)],[c_743,c_147183]) ).

tcf(c_160421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Relation_ODomain(X0,X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_147183,c_841]) ).

tcf(c_160434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_147218,c_841]) ).

tcf(c_160435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X3),X4)),
    inference(superposition,[status(thm)],[c_743,c_147293]) ).

tcf(c_160442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_147293,c_841]) ).

tcf(c_160448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_147392,c_841]) ).

tcf(c_160449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X3),X4)),
    inference(superposition,[status(thm)],[c_743,c_147452]) ).

tcf(c_160455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),
    inference(superposition,[status(thm)],[c_147452,c_841]) ).

tcf(c_160462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),
    inference(superposition,[status(thm)],[c_147764,c_841]) ).

tcf(c_160464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_147806,c_144852]) ).

tcf(c_160465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_147806,c_125973]) ).

tcf(c_160466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_147806,c_125887]) ).

tcf(c_160467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147806,c_633]) ).

tcf(c_160468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_147806,c_776]) ).

tcf(c_160469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_147806,c_762]) ).

tcf(c_160470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_147806,c_761]) ).

tcf(c_160471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147806,c_797]) ).

tcf(c_160475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_147806,c_796]) ).

tcf(c_160476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_147806,c_642]) ).

tcf(c_160477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_147806,c_774]) ).

tcf(c_160478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_147806,c_770]) ).

tcf(c_160479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_147806,c_768]) ).

tcf(c_160480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_147806,c_763]) ).

tcf(c_160538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_147809,c_144852]) ).

tcf(c_160539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_147809,c_125973]) ).

tcf(c_160540,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_147809,c_125887]) ).

tcf(c_160541,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147809,c_633]) ).

tcf(c_160542,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_147809,c_776]) ).

tcf(c_160543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_147809,c_762]) ).

tcf(c_160544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_147809,c_761]) ).

tcf(c_160545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147809,c_797]) ).

tcf(c_160549,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_147809,c_796]) ).

tcf(c_160550,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_147809,c_642]) ).

tcf(c_160551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_147809,c_774]) ).

tcf(c_160552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_147809,c_770]) ).

tcf(c_160553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_147809,c_768]) ).

tcf(c_160554,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_147809,c_763]) ).

tcf(c_160607,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_147821,c_560]) ).

tcf(c_160608,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_147821,c_564]) ).

tcf(c_160609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_147821,c_562]) ).

tcf(c_160610,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_147821,c_561]) ).

tcf(c_160611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_147821,c_565]) ).

tcf(c_160612,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_147821,c_144852]) ).

tcf(c_160613,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_147821,c_125973]) ).

tcf(c_160614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_147821,c_125887]) ).

tcf(c_160615,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147821,c_633]) ).

tcf(c_160617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_147821,c_762]) ).

tcf(c_160619,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147821,c_797]) ).

tcf(c_160623,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_147821,c_796]) ).

tcf(c_160624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147821,c_642]) ).

tcf(c_160625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_147821,c_774]) ).

tcf(c_160626,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_147821,c_770]) ).

tcf(c_160627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_147821,c_768]) ).

tcf(c_160628,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_147821,c_763]) ).

tcf(c_160741,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160627,c_562]) ).

tcf(c_160742,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160627,c_561]) ).

tcf(c_160743,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_160627,c_565]) ).

tcf(c_160744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_160627,c_144852]) ).

tcf(c_160745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_160627,c_125973]) ).

tcf(c_160746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_160627,c_125887]) ).

tcf(c_160747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160627,c_633]) ).

tcf(c_160748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_160627,c_776]) ).

tcf(c_160749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_160627,c_762]) ).

tcf(c_160751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160627,c_642]) ).

tcf(c_160752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160627,c_774]) ).

tcf(c_160753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_160627,c_770]) ).

tcf(c_160754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_160627,c_768]) ).

tcf(c_160755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_160627,c_763]) ).

tcf(c_160756,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_160627,c_840]) ).

tcf(c_160757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_160627,c_126501]) ).

tcf(c_160775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_160751,c_160627]) ).

tcf(c_160778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_160747,c_160627]) ).

tcf(c_160787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_160756,c_841]) ).

tcf(c_160796,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160787,c_562]) ).

tcf(c_160797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160787,c_561]) ).

tcf(c_160798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_160787,c_565]) ).

tcf(c_160799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_160787,c_144852]) ).

tcf(c_160800,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_160787,c_125973]) ).

tcf(c_160801,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_160787,c_125887]) ).

tcf(c_160802,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160787,c_633]) ).

tcf(c_160803,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_160787,c_776]) ).

tcf(c_160804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_160787,c_762]) ).

tcf(c_160806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160787,c_642]) ).

tcf(c_160807,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160787,c_774]) ).

tcf(c_160808,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_160787,c_770]) ).

tcf(c_160809,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_160787,c_768]) ).

tcf(c_160810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_160787,c_763]) ).

tcf(c_160830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_160806,c_160787]) ).

tcf(c_160833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_160802,c_160787]) ).

tcf(c_160855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X0,X8,X9,X5,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,iPr_def_10),X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X5,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X6,iPr_def_10),X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(light_normalisation,[status(thm)],[c_585,c_7263,c_7265]) ).

tcf(c_160865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(c_Expr_Oexp_OVal(X5,iPr_def_10),X6,X7,X0,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_125781,c_160855]) ).

tcf(c_160874,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),
    inference(superposition,[status(thm)],[c_147843,c_841]) ).

tcf(c_160878,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_147937,c_144852]) ).

tcf(c_160879,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_147937,c_125973]) ).

tcf(c_160880,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_147937,c_125887]) ).

tcf(c_160881,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147937,c_633]) ).

tcf(c_160882,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_147937,c_776]) ).

tcf(c_160883,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_147937,c_762]) ).

tcf(c_160884,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_147937,c_761]) ).

tcf(c_160885,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147937,c_797]) ).

tcf(c_160889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_147937,c_796]) ).

tcf(c_160890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_147937,c_642]) ).

tcf(c_160891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_147937,c_774]) ).

tcf(c_160892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_147937,c_770]) ).

tcf(c_160893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_147937,c_768]) ).

tcf(c_160894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_147937,c_763]) ).

tcf(c_160928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_147943,c_144852]) ).

tcf(c_160929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_147943,c_125973]) ).

tcf(c_160930,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_147943,c_125887]) ).

tcf(c_160931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147943,c_633]) ).

tcf(c_160932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_147943,c_776]) ).

tcf(c_160933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_147943,c_762]) ).

tcf(c_160934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_147943,c_761]) ).

tcf(c_160935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_147943,c_797]) ).

tcf(c_160939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_147943,c_796]) ).

tcf(c_160940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_147943,c_642]) ).

tcf(c_160941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_147943,c_774]) ).

tcf(c_160942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_147943,c_770]) ).

tcf(c_160943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_147943,c_768]) ).

tcf(c_160944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_147943,c_763]) ).

tcf(c_161017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148190,c_560]) ).

tcf(c_161018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148190,c_564]) ).

tcf(c_161019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148190,c_562]) ).

tcf(c_161020,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148190,c_561]) ).

tcf(c_161021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_148190,c_565]) ).

tcf(c_161022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_148190,c_144852]) ).

tcf(c_161023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_148190,c_125973]) ).

tcf(c_161024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_148190,c_125887]) ).

tcf(c_161025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148190,c_633]) ).

tcf(c_161027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_148190,c_762]) ).

tcf(c_161029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148190,c_797]) ).

tcf(c_161033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_148190,c_796]) ).

tcf(c_161034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148190,c_642]) ).

tcf(c_161035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_148190,c_774]) ).

tcf(c_161036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_148190,c_770]) ).

tcf(c_161037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_148190,c_768]) ).

tcf(c_161038,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_148190,c_763]) ).

tcf(c_161102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161037,c_562]) ).

tcf(c_161103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161037,c_561]) ).

tcf(c_161104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161037,c_565]) ).

tcf(c_161105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_161037,c_144852]) ).

tcf(c_161106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_161037,c_125973]) ).

tcf(c_161107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_161037,c_125887]) ).

tcf(c_161108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161037,c_633]) ).

tcf(c_161109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161037,c_776]) ).

tcf(c_161110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_161037,c_762]) ).

tcf(c_161112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161037,c_642]) ).

tcf(c_161113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161037,c_774]) ).

tcf(c_161114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_161037,c_770]) ).

tcf(c_161115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_161037,c_768]) ).

tcf(c_161116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_161037,c_763]) ).

tcf(c_161117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_161037,c_840]) ).

tcf(c_161118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_161037,c_126501]) ).

tcf(c_161136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_161112,c_161037]) ).

tcf(c_161139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_161108,c_161037]) ).

tcf(c_161169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_161117,c_841]) ).

tcf(c_161179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161169,c_562]) ).

tcf(c_161180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161169,c_561]) ).

tcf(c_161181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_161169,c_565]) ).

tcf(c_161182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_161169,c_144852]) ).

tcf(c_161183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_161169,c_125973]) ).

tcf(c_161184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_161169,c_125887]) ).

tcf(c_161185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161169,c_633]) ).

tcf(c_161186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_161169,c_776]) ).

tcf(c_161187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_161169,c_762]) ).

tcf(c_161189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161169,c_642]) ).

tcf(c_161190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161169,c_774]) ).

tcf(c_161191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_161169,c_770]) ).

tcf(c_161192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_161169,c_768]) ).

tcf(c_161193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_161169,c_763]) ).

tcf(c_161213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_161189,c_161169]) ).

tcf(c_161216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_161185,c_161169]) ).

tcf(c_161271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),
    inference(superposition,[status(thm)],[c_148250,c_841]) ).

tcf(c_161276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148283,c_560]) ).

tcf(c_161277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148283,c_564]) ).

tcf(c_161278,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4)),c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148283,c_562]) ).

tcf(c_161279,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4))))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,t_a),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148283,c_561]) ).

tcf(c_161280,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2),X2) ),
    inference(superposition,[status(thm)],[c_148283,c_565]) ).

tcf(c_161281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_148283,c_144852]) ).

tcf(c_161282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_148283,c_125973]) ).

tcf(c_161283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5),c_Pair(X6,X6,X1,X1))),
    inference(superposition,[status(thm)],[c_148283,c_125887]) ).

tcf(c_161284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148283,c_633]) ).

tcf(c_161286,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2) ),
    inference(superposition,[status(thm)],[c_148283,c_762]) ).

tcf(c_161288,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148283,c_797]) ).

tcf(c_161292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X3),X4),X1),tc_prod(X1,X1)),
    inference(superposition,[status(thm)],[c_148283,c_796]) ).

tcf(c_161293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0 = X1 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148283,c_642]) ).

tcf(c_161294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X2),X4),X5),X6),X1,X2,X2),X2)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_148283,c_774]) ).

tcf(c_161295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2,X2),X2),
    inference(superposition,[status(thm)],[c_148283,c_770]) ).

tcf(c_161296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X2),
    inference(superposition,[status(thm)],[c_148283,c_768]) ).

tcf(c_161297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(c_Pair(X7,X7,X1,X1),c_Pair(X7,X7,X1,X1),X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X5,X6) ),
    inference(superposition,[status(thm)],[c_148283,c_763]) ).

tcf(c_161361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161296,c_562]) ).

tcf(c_161362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(t_a,t_a)),X2),X3),X4),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161296,c_561]) ).

tcf(c_161363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161296,c_565]) ).

tcf(c_161364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X6),
    inference(superposition,[status(thm)],[c_161296,c_144852]) ).

tcf(c_161365,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_161296,c_125973]) ).

tcf(c_161366,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X1)),X2),X3),X4),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X5)),
    inference(superposition,[status(thm)],[c_161296,c_125887]) ).

tcf(c_161367,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161296,c_633]) ).

tcf(c_161368,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161296,c_776]) ).

tcf(c_161369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X2)),X3),X4),X5),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_161296,c_762]) ).

tcf(c_161371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X3)),X5),X6),X7),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161296,c_642]) ).

tcf(c_161372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,tc_prod(X2,X5)),X6),X7),X8),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161296,c_774]) ).

tcf(c_161373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_161296,c_770]) ).

tcf(c_161374,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,tc_prod(X2,X3)),X4),X5),X6),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2),
    inference(superposition,[status(thm)],[c_161296,c_768]) ).

tcf(c_161375,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X1) ),
    inference(superposition,[status(thm)],[c_161296,c_763]) ).

tcf(c_161376,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5)),
    inference(superposition,[status(thm)],[c_161296,c_840]) ).

tcf(c_161377,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,iPr_def_13),X2),X3),X4),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11),
    inference(superposition,[status(thm)],[c_161296,c_126501]) ).

tcf(c_161395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,tc_prod(X1,X2)),X3),X4),X5),tc_prod(X1,X2),tc_prod(X1,X2)),X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_161371,c_161296]) ).

tcf(c_161398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,tc_prod(X2,X2)),X4),X5),X6),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_161367,c_161296]) ).

tcf(c_161474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),
    inference(superposition,[status(thm)],[c_161376,c_841]) ).

tcf(c_161482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X0))
      | c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161474,c_562]) ).

tcf(c_161483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161474,c_561]) ).

tcf(c_161484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_161474,c_565]) ).

tcf(c_161485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X7),
    inference(superposition,[status(thm)],[c_161474,c_144852]) ).

tcf(c_161486,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_161474,c_125973]) ).

tcf(c_161487,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5),X6)),
    inference(superposition,[status(thm)],[c_161474,c_125887]) ).

tcf(c_161488,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161474,c_633]) ).

tcf(c_161489,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6),X6) ),
    inference(superposition,[status(thm)],[c_161474,c_776]) ).

tcf(c_161490,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X6)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6) ),
    inference(superposition,[status(thm)],[c_161474,c_762]) ).

tcf(c_161492,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161474,c_642]) ).

tcf(c_161493,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X8),X5,X5),X1,X2,X9),X9)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161474,c_774]) ).

tcf(c_161494,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X7,X6),X7),
    inference(superposition,[status(thm)],[c_161474,c_770]) ).

tcf(c_161495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X5),X2,X2),X6,X7),X6),
    inference(superposition,[status(thm)],[c_161474,c_768]) ).

tcf(c_161496,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X7,X6,X6),X5,tc_prod(X6,X6))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(superposition,[status(thm)],[c_161474,c_763]) ).

tcf(c_161516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X7 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X4),X1,X1),X5,X6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_161492,c_161474]) ).

tcf(c_161519,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X7),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_161488,c_161474]) ).

tcf(c_161527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),
    inference(superposition,[status(thm)],[c_148323,c_841]) ).

tcf(c_161532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_148651,c_144852]) ).

tcf(c_161533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_148651,c_125973]) ).

tcf(c_161534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_148651,c_125887]) ).

tcf(c_161535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148651,c_633]) ).

tcf(c_161536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_148651,c_776]) ).

tcf(c_161537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_148651,c_762]) ).

tcf(c_161538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_148651,c_761]) ).

tcf(c_161539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148651,c_797]) ).

tcf(c_161543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_148651,c_796]) ).

tcf(c_161544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_148651,c_642]) ).

tcf(c_161545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_148651,c_774]) ).

tcf(c_161546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_148651,c_770]) ).

tcf(c_161547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_148651,c_768]) ).

tcf(c_161548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_148651,c_763]) ).

tcf(c_161625,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_148661]) ).

tcf(c_161628,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_148661]) ).

tcf(c_161629,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_Oconverse(X0,X1,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X1) ),
    inference(superposition,[status(thm)],[c_148661,c_511]) ).

tcf(c_161630,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(X2,c_Relation_ODomain(X1,t_a,t_a),t_a)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_Oconverse(X1,t_a,t_a)))) ),
    inference(superposition,[status(thm)],[c_148661,c_553]) ).

tcf(c_161631,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_Oconverse(X0,X1,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X1) ),
    inference(superposition,[status(thm)],[c_148661,c_545]) ).

tcf(c_161632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Relation_ODomain(X1,X2,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_Oconverse(X1,X2,X2),X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_148661,c_550]) ).

tcf(c_161633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148661,c_560]) ).

tcf(c_161634,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148661,c_564]) ).

tcf(c_161635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148661,c_562]) ).

tcf(c_161636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148661,c_561]) ).

tcf(c_161637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_148661,c_565]) ).

tcf(c_161638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_148661,c_144852]) ).

tcf(c_161639,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_148661,c_125973]) ).

tcf(c_161640,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_148661,c_125887]) ).

tcf(c_161641,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X2,X2),c_Relation_ODomain(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_148661,c_633]) ).

tcf(c_161642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2)
      | c_in(c_Pair(X3,X0,X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_148661,c_776]) ).

tcf(c_161643,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_148661,c_762]) ).

tcf(c_161644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_148661,c_761]) ).

tcf(c_161645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X3),c_Relation_ODomain(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_148661,c_642]) ).

tcf(c_161646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X3,X2,X5),c_Relation_ODomain(X4,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5))
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_148661,c_774]) ).

tcf(c_161647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X2,X3),c_Relation_ODomain(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_148661,c_770]) ).

tcf(c_161648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X4,X2,X3),c_Relation_ODomain(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_148661,c_768]) ).

tcf(c_161649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Relation_ODomain(X0,X1,X1),X1)
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_148661,c_763]) ).

tcf(c_161650,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,X1,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_148661,c_840]) ).

tcf(c_161651,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(c_Pair(X0,X2,iPr_def_11,iPr_def_12),c_Relation_ODomain(X1,iPr_def_13,iPr_def_13),iPr_def_13)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,iPr_def_13,iPr_def_13),iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_148661,c_126501]) ).

tcf(c_161800,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X0,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1),X2)) ),
    inference(superposition,[status(thm)],[c_596,c_148681]) ).

tcf(c_161801,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,X2,X2),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_670,c_148681]) ).

tcf(c_161802,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(c_Relation_OId__on(X0,X1),X1,X1),X2)) ),
    inference(superposition,[status(thm)],[c_684,c_148681]) ).

tcf(c_161803,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1,X1),X2)) ),
    inference(superposition,[status(thm)],[c_687,c_148681]) ).

tcf(c_161804,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(X2,X3,X3),X3,X3),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Relation_ODomain(c_Relation_Oconverse(X2,X3,X3),X3,X3),X1),c_Wellfounded_Oacc(X2,X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_148681,c_517]) ).

tcf(c_161805,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(X3,X4,X4),X4,X4),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Relation_ODomain(c_Relation_Oconverse(X3,X4,X4),X4,X4),X1,X2),c_Wellfounded_Oacc(X3,X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_148681,c_537]) ).

tcf(c_161806,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_148681,c_841]) ).

tcf(c_161811,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(light_normalisation,[status(thm)],[c_161802,c_724]) ).

tcf(c_161843,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X1,X2))
      | hBOOL(hAPP(X0,X2))
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a)))) ),
    inference(superposition,[status(thm)],[c_161811,c_553]) ).

tcf(c_161845,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X3))
      | hBOOL(hAPP(X0,X3))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_OId__on(X1,X2),X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_161811,c_550]) ).

tcf(c_161846,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161811,c_560]) ).

tcf(c_161847,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X1,c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161811,c_564]) ).

tcf(c_161848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161811,c_562]) ).

tcf(c_161849,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(X1,c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161811,c_561]) ).

tcf(c_161850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X1,c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161811,c_565]) ).

tcf(c_161851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_161811,c_144852]) ).

tcf(c_161852,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_161811,c_125973]) ).

tcf(c_161853,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_161811,c_125887]) ).

tcf(c_161854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X4,X0,X2,X2)))
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,tc_prod(X2,X2)),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161811,c_633]) ).

tcf(c_161855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X3,X0,X2,X2)))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161811,c_776]) ).

tcf(c_161856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | hBOOL(hAPP(X1,c_Pair(X3,X4,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_161811,c_762]) ).

tcf(c_161857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X2)
      | hBOOL(hAPP(X1,c_Pair(X3,X4,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_161811,c_761]) ).

tcf(c_161858,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X5,X2,X3)))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X3)),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161811,c_642]) ).

tcf(c_161859,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X3,X2,X5)))
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X5)),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161811,c_774]) ).

tcf(c_161860,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X4,X0,X2,X3)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_161811,c_770]) ).

tcf(c_161861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X4,X2,X3)))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_161811,c_768]) ).

tcf(c_161862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_161811,c_763]) ).

tcf(c_161863,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_161811,c_840]) ).

tcf(c_161864,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X2,iPr_def_11,iPr_def_12)))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,iPr_def_13),iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_161811,c_126501]) ).

tcf(c_161972,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161863,c_517]) ).

tcf(c_161973,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_161863,c_537]) ).

tcf(c_161974,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_161863,c_841]) ).

tcf(c_161997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161974,c_560]) ).

tcf(c_161998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X1,c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161974,c_564]) ).

tcf(c_161999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161974,c_562]) ).

tcf(c_162000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(X1,c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161974,c_561]) ).

tcf(c_162001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X1,c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3,X3)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_161974,c_565]) ).

tcf(c_162002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_161974,c_144852]) ).

tcf(c_162003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_161974,c_125973]) ).

tcf(c_162004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_161974,c_125887]) ).

tcf(c_162005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X5,X0,X2,X2)))
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161974,c_633]) ).

tcf(c_162006,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X4,X0,X3,X3)))
      | c_in(X4,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_161974,c_776]) ).

tcf(c_162007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X3)
      | hBOOL(hAPP(X1,c_Pair(X4,X5,X3,X3)))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_161974,c_762]) ).

tcf(c_162008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X3)
      | hBOOL(hAPP(X1,c_Pair(X4,X5,X3,X3)))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_161974,c_761]) ).

tcf(c_162009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X6,X2,X3)))
      | ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161974,c_642]) ).

tcf(c_162010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X3,X2,X6)))
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161974,c_774]) ).

tcf(c_162011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X5,X0,X3,X4)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_161974,c_770]) ).

tcf(c_162012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X5,X3,X4)))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3,X4),X3) ),
    inference(superposition,[status(thm)],[c_161974,c_768]) ).

tcf(c_162013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_161974,c_763]) ).

tcf(c_162150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162002,c_560]) ).

tcf(c_162151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162002,c_564]) ).

tcf(c_162152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162002,c_562]) ).

tcf(c_162153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162002,c_561]) ).

tcf(c_162154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X1,c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4,X4)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_162002,c_565]) ).

tcf(c_162155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162002,c_144852]) ).

tcf(c_162156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_162002,c_125973]) ).

tcf(c_162157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_162002,c_125887]) ).

tcf(c_162158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X5,X2,X2)))
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_793]) ).

tcf(c_162159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X1,X5,X4,X4)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X4,X4),c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162002,c_632]) ).

tcf(c_162160,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X5,X1,X4,X4)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X4,X4),c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162002,c_631]) ).

tcf(c_162161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X5,X0,X2,X2)))
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_847]) ).

tcf(c_162162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X5,X1,X4,X4)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X1,X4,X4),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162002,c_799]) ).

tcf(c_162163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X5,X0,X2,X2)))
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_798]) ).

tcf(c_162164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X1,X5,X4,X4)))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X4,X4),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X4,X4))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162002,c_795]) ).

tcf(c_162165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X5,X0,X2,X2)))
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_849]) ).

tcf(c_162166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X1,X5,X2,X2)))
      | c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_848]) ).

tcf(c_162168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X1,X5,X2,X2)))
      | c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_781]) ).

tcf(c_162169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X1,X5,X4,X4)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4))) ),
    inference(superposition,[status(thm)],[c_162002,c_794]) ).

tcf(c_162170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X5,X1,X4,X4)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4))) ),
    inference(superposition,[status(thm)],[c_162002,c_784]) ).

tcf(c_162171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X5,X1,X4,X4)))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162002,c_800]) ).

tcf(c_162172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X2,c_Pair(X1,X5,X4,X4)))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162002,c_786]) ).

tcf(c_162173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X1,X2,X2)))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_162002,c_789]) ).

tcf(c_162175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X2,c_Pair(X0,X1,X4,X4)))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4,X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_162002,c_806]) ).

tcf(c_162176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162002,c_633]) ).

tcf(c_162177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X5,X0,X4,X4)))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_162002,c_776]) ).

tcf(c_162178,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | hBOOL(hAPP(X1,c_Pair(X5,X6,X4,X4)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_162002,c_762]) ).

tcf(c_162179,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,X0,X4)
      | hBOOL(hAPP(X1,c_Pair(X5,X6,X4,X4)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_162002,c_761]) ).

tcf(c_162180,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X7,X2,X3)))
      | ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162002,c_642]) ).

tcf(c_162181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X3,X2,X7)))
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162002,c_774]) ).

tcf(c_162182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X6,X0,X4,X5)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X5,X4),X5) ),
    inference(superposition,[status(thm)],[c_162002,c_770]) ).

tcf(c_162183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X6,X4,X5)))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X4) ),
    inference(superposition,[status(thm)],[c_162002,c_768]) ).

tcf(c_162184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_162002,c_763]) ).

tcf(c_162538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162003,c_517]) ).

tcf(c_162539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_162003,c_537]) ).

tcf(c_162551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162004,c_517]) ).

tcf(c_162552,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_162004,c_537]) ).

tcf(c_162553,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_162004,c_841]) ).

tcf(c_162566,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162553,c_560]) ).

tcf(c_162567,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162553,c_564]) ).

tcf(c_162568,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X0))
      | c_in(X4,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162553,c_562]) ).

tcf(c_162569,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(X1,c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X5,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162553,c_561]) ).

tcf(c_162570,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X1,c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X6,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4,X4)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_162553,c_565]) ).

tcf(c_162571,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162553,c_144852]) ).

tcf(c_162572,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_162553,c_125973]) ).

tcf(c_162573,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X4))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4)) ),
    inference(superposition,[status(thm)],[c_162553,c_125887]) ).

tcf(c_162574,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162553,c_633]) ).

tcf(c_162575,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X5,X0,X4,X4)))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X4) ),
    inference(superposition,[status(thm)],[c_162553,c_776]) ).

tcf(c_162576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X4)
      | hBOOL(hAPP(X1,c_Pair(X5,X6,X4,X4)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_162553,c_762]) ).

tcf(c_162577,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,X0,X4)
      | hBOOL(hAPP(X1,c_Pair(X5,X6,X4,X4)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_162553,c_761]) ).

tcf(c_162578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X5,X0,X2,X2)))
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162553,c_797]) ).

tcf(c_162582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X1,X2,X2)))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162553,c_796]) ).

tcf(c_162583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X7,X2,X3)))
      | ( X1 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162553,c_642]) ).

tcf(c_162584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X3,X2,X7)))
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X1,X2,X7),X7)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162553,c_774]) ).

tcf(c_162585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X6,X0,X4,X5)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X5,X4),X5) ),
    inference(superposition,[status(thm)],[c_162553,c_770]) ).

tcf(c_162586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X6,X4,X5)))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4,X5),X4) ),
    inference(superposition,[status(thm)],[c_162553,c_768]) ).

tcf(c_162587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | c_in(c_Pair(X5,X5,X4,X4),X3,tc_prod(X4,X4))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3,X4) ),
    inference(superposition,[status(thm)],[c_162553,c_763]) ).

tcf(c_162698,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X2,X3),X3,X2),X4),
    inference(superposition,[status(thm)],[c_148833,c_841]) ).

tcf(c_162700,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_687,c_148888]) ).

tcf(c_162706,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),
    inference(superposition,[status(thm)],[c_148888,c_841]) ).

tcf(c_162707,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_596,c_148956]) ).

tcf(c_162714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),
    inference(superposition,[status(thm)],[c_148956,c_841]) ).

tcf(c_162715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_596,c_149128]) ).

tcf(c_162722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),
    inference(superposition,[status(thm)],[c_149128,c_841]) ).

tcf(c_162724,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1),X1,X1),X3)),
    inference(superposition,[status(thm)],[c_687,c_149189]) ).

tcf(c_162731,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),
    inference(superposition,[status(thm)],[c_149189,c_841]) ).

tcf(c_162735,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_149274,c_144852]) ).

tcf(c_162736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149274,c_125973]) ).

tcf(c_162737,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149274,c_125887]) ).

tcf(c_162738,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149274,c_633]) ).

tcf(c_162739,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_149274,c_776]) ).

tcf(c_162740,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149274,c_762]) ).

tcf(c_162741,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149274,c_761]) ).

tcf(c_162742,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149274,c_797]) ).

tcf(c_162746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149274,c_796]) ).

tcf(c_162747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149274,c_642]) ).

tcf(c_162748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149274,c_774]) ).

tcf(c_162749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_149274,c_770]) ).

tcf(c_162750,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_149274,c_768]) ).

tcf(c_162751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_149274,c_763]) ).

tcf(c_162810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149483,c_144852]) ).

tcf(c_162811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149483,c_125973]) ).

tcf(c_162812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149483,c_125887]) ).

tcf(c_162813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149483,c_633]) ).

tcf(c_162814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149483,c_776]) ).

tcf(c_162815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149483,c_762]) ).

tcf(c_162816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149483,c_761]) ).

tcf(c_162817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149483,c_797]) ).

tcf(c_162821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149483,c_796]) ).

tcf(c_162822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149483,c_642]) ).

tcf(c_162823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149483,c_774]) ).

tcf(c_162824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149483,c_770]) ).

tcf(c_162825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149483,c_768]) ).

tcf(c_162826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149483,c_763]) ).

tcf(c_162942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149496,c_144852]) ).

tcf(c_162943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149496,c_125973]) ).

tcf(c_162944,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149496,c_125887]) ).

tcf(c_162945,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149496,c_633]) ).

tcf(c_162946,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149496,c_776]) ).

tcf(c_162947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149496,c_762]) ).

tcf(c_162948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149496,c_761]) ).

tcf(c_162949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149496,c_797]) ).

tcf(c_162953,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149496,c_796]) ).

tcf(c_162954,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149496,c_642]) ).

tcf(c_162955,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149496,c_774]) ).

tcf(c_162956,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149496,c_770]) ).

tcf(c_162957,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149496,c_768]) ).

tcf(c_162958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149496,c_763]) ).

tcf(c_163010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_149506,c_144852]) ).

tcf(c_163011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149506,c_125973]) ).

tcf(c_163012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149506,c_125887]) ).

tcf(c_163013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149506,c_633]) ).

tcf(c_163014,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_149506,c_776]) ).

tcf(c_163015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149506,c_762]) ).

tcf(c_163016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149506,c_761]) ).

tcf(c_163017,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149506,c_797]) ).

tcf(c_163021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149506,c_796]) ).

tcf(c_163022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149506,c_642]) ).

tcf(c_163023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149506,c_774]) ).

tcf(c_163024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_149506,c_770]) ).

tcf(c_163025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_149506,c_768]) ).

tcf(c_163026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_149506,c_763]) ).

tcf(c_163061,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_149515,c_144852]) ).

tcf(c_163062,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149515,c_125973]) ).

tcf(c_163063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149515,c_125887]) ).

tcf(c_163064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149515,c_633]) ).

tcf(c_163065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_149515,c_776]) ).

tcf(c_163066,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149515,c_762]) ).

tcf(c_163067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149515,c_761]) ).

tcf(c_163068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149515,c_797]) ).

tcf(c_163072,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149515,c_796]) ).

tcf(c_163073,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149515,c_642]) ).

tcf(c_163074,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149515,c_774]) ).

tcf(c_163075,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_149515,c_770]) ).

tcf(c_163076,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_149515,c_768]) ).

tcf(c_163077,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_149515,c_763]) ).

tcf(c_163136,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_149531,c_144852]) ).

tcf(c_163137,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149531,c_125973]) ).

tcf(c_163138,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149531,c_125887]) ).

tcf(c_163139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149531,c_633]) ).

tcf(c_163140,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_149531,c_776]) ).

tcf(c_163141,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149531,c_762]) ).

tcf(c_163142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149531,c_761]) ).

tcf(c_163143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149531,c_797]) ).

tcf(c_163147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149531,c_796]) ).

tcf(c_163148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149531,c_642]) ).

tcf(c_163149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149531,c_774]) ).

tcf(c_163150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_149531,c_770]) ).

tcf(c_163151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_149531,c_768]) ).

tcf(c_163152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_149531,c_763]) ).

tcf(c_163258,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),X0),X3),X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_149555,c_144852]) ).

tcf(c_163259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149555,c_125973]) ).

tcf(c_163260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7),X2)),
    inference(superposition,[status(thm)],[c_149555,c_125887]) ).

tcf(c_163261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X9),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149555,c_633]) ).

tcf(c_163262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X4)),X5),X6),X7),X8),X4),X4) ),
    inference(superposition,[status(thm)],[c_149555,c_776]) ).

tcf(c_163263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X4,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149555,c_762]) ).

tcf(c_163264,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X4,X5,X5)),X6),X7),X8),X9),X5) ),
    inference(superposition,[status(thm)],[c_149555,c_761]) ).

tcf(c_163265,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X5,X0,X2,X2)),X6),X7),X8),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149555,c_797]) ).

tcf(c_163269,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X3,X4),c_Pair(X0,X1,X2,X2)),X5),X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149555,c_796]) ).

tcf(c_163270,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X6,X2,X3)),X7),X8),X9),X10),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149555,c_642]) ).

tcf(c_163271,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X4,X5),c_Pair(X0,X3,X2,X6)),X7),X8),X9),X10),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149555,c_774]) ).

tcf(c_163272,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X3,X0,X4,X5)),X6),X7),X8),X9),X4,X5),X5,X4),X5),
    inference(superposition,[status(thm)],[c_149555,c_770]) ).

tcf(c_163273,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X1,X2),c_Pair(X0,X3,X4,X5)),X6),X7),X8),X9),X4,X5),X4),
    inference(superposition,[status(thm)],[c_149555,c_768]) ).

tcf(c_163274,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X2,X2,X8,X8),X7,tc_prod(X8,X8))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(c_TypeRel_Owiden(X0,X1),X2),X3),X4),X5),X6),X7,X8) ),
    inference(superposition,[status(thm)],[c_149555,c_763]) ).

tcf(c_163298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149729,c_144852]) ).

tcf(c_163299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149729,c_125973]) ).

tcf(c_163300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149729,c_125887]) ).

tcf(c_163301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149729,c_633]) ).

tcf(c_163302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149729,c_776]) ).

tcf(c_163303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149729,c_762]) ).

tcf(c_163304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149729,c_761]) ).

tcf(c_163305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149729,c_797]) ).

tcf(c_163309,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149729,c_796]) ).

tcf(c_163310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149729,c_642]) ).

tcf(c_163311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149729,c_774]) ).

tcf(c_163312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149729,c_770]) ).

tcf(c_163313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149729,c_768]) ).

tcf(c_163314,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149729,c_763]) ).

tcf(c_163357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149738,c_144852]) ).

tcf(c_163358,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149738,c_125973]) ).

tcf(c_163359,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149738,c_125887]) ).

tcf(c_163360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149738,c_633]) ).

tcf(c_163361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149738,c_776]) ).

tcf(c_163362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149738,c_762]) ).

tcf(c_163363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149738,c_761]) ).

tcf(c_163364,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149738,c_797]) ).

tcf(c_163368,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149738,c_796]) ).

tcf(c_163369,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149738,c_642]) ).

tcf(c_163370,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149738,c_774]) ).

tcf(c_163371,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149738,c_770]) ).

tcf(c_163372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149738,c_768]) ).

tcf(c_163373,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149738,c_763]) ).

tcf(c_163415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149754,c_144852]) ).

tcf(c_163416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149754,c_125973]) ).

tcf(c_163417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149754,c_125887]) ).

tcf(c_163418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149754,c_633]) ).

tcf(c_163419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149754,c_776]) ).

tcf(c_163420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149754,c_762]) ).

tcf(c_163421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149754,c_761]) ).

tcf(c_163422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149754,c_797]) ).

tcf(c_163426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149754,c_796]) ).

tcf(c_163427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149754,c_642]) ).

tcf(c_163428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149754,c_774]) ).

tcf(c_163429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149754,c_770]) ).

tcf(c_163430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149754,c_768]) ).

tcf(c_163431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149754,c_763]) ).

tcf(c_163532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149761,c_144852]) ).

tcf(c_163533,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149761,c_125973]) ).

tcf(c_163534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149761,c_125887]) ).

tcf(c_163535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149761,c_633]) ).

tcf(c_163536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149761,c_776]) ).

tcf(c_163537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149761,c_762]) ).

tcf(c_163538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149761,c_761]) ).

tcf(c_163539,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149761,c_797]) ).

tcf(c_163543,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149761,c_796]) ).

tcf(c_163544,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149761,c_642]) ).

tcf(c_163545,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149761,c_774]) ).

tcf(c_163546,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149761,c_770]) ).

tcf(c_163547,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149761,c_768]) ).

tcf(c_163548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149761,c_763]) ).

tcf(c_163578,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149771,c_144852]) ).

tcf(c_163579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149771,c_125973]) ).

tcf(c_163580,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149771,c_125887]) ).

tcf(c_163581,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149771,c_633]) ).

tcf(c_163582,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149771,c_776]) ).

tcf(c_163583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149771,c_762]) ).

tcf(c_163584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149771,c_761]) ).

tcf(c_163585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149771,c_797]) ).

tcf(c_163589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149771,c_796]) ).

tcf(c_163590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149771,c_642]) ).

tcf(c_163591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149771,c_774]) ).

tcf(c_163592,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149771,c_770]) ).

tcf(c_163593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149771,c_768]) ).

tcf(c_163594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149771,c_763]) ).

tcf(c_163810,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_149797,c_144852]) ).

tcf(c_163811,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149797,c_125973]) ).

tcf(c_163812,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_149797,c_125887]) ).

tcf(c_163813,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149797,c_633]) ).

tcf(c_163814,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_149797,c_776]) ).

tcf(c_163815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149797,c_762]) ).

tcf(c_163816,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_149797,c_761]) ).

tcf(c_163817,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_149797,c_797]) ).

tcf(c_163821,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_149797,c_796]) ).

tcf(c_163822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_149797,c_642]) ).

tcf(c_163823,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_149797,c_774]) ).

tcf(c_163824,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_149797,c_770]) ).

tcf(c_163825,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_149797,c_768]) ).

tcf(c_163826,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_149797,c_763]) ).

tcf(c_163850,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150318,c_144852]) ).

tcf(c_163851,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150318,c_125973]) ).

tcf(c_163852,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150318,c_125887]) ).

tcf(c_163853,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150318,c_633]) ).

tcf(c_163854,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_150318,c_776]) ).

tcf(c_163855,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150318,c_762]) ).

tcf(c_163856,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150318,c_761]) ).

tcf(c_163857,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150318,c_797]) ).

tcf(c_163861,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150318,c_796]) ).

tcf(c_163862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150318,c_642]) ).

tcf(c_163863,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150318,c_774]) ).

tcf(c_163864,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_150318,c_770]) ).

tcf(c_163865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_150318,c_768]) ).

tcf(c_163866,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150318,c_763]) ).

tcf(c_163888,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150325,c_144852]) ).

tcf(c_163889,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150325,c_125973]) ).

tcf(c_163890,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150325,c_125887]) ).

tcf(c_163891,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150325,c_633]) ).

tcf(c_163892,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_150325,c_776]) ).

tcf(c_163893,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150325,c_762]) ).

tcf(c_163894,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150325,c_761]) ).

tcf(c_163895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150325,c_797]) ).

tcf(c_163899,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150325,c_796]) ).

tcf(c_163900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150325,c_642]) ).

tcf(c_163901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150325,c_774]) ).

tcf(c_163902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_150325,c_770]) ).

tcf(c_163903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_150325,c_768]) ).

tcf(c_163904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150325,c_763]) ).

tcf(c_163936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150335,c_144852]) ).

tcf(c_163937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150335,c_125973]) ).

tcf(c_163938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150335,c_125887]) ).

tcf(c_163939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150335,c_633]) ).

tcf(c_163940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_150335,c_776]) ).

tcf(c_163941,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150335,c_762]) ).

tcf(c_163942,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150335,c_761]) ).

tcf(c_163943,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150335,c_797]) ).

tcf(c_163947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150335,c_796]) ).

tcf(c_163948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150335,c_642]) ).

tcf(c_163949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150335,c_774]) ).

tcf(c_163950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_150335,c_770]) ).

tcf(c_163951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_150335,c_768]) ).

tcf(c_163952,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150335,c_763]) ).

tcf(c_163997,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150344,c_144852]) ).

tcf(c_163998,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150344,c_125973]) ).

tcf(c_163999,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150344,c_125887]) ).

tcf(c_164000,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150344,c_633]) ).

tcf(c_164001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_150344,c_776]) ).

tcf(c_164002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150344,c_762]) ).

tcf(c_164003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150344,c_761]) ).

tcf(c_164004,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150344,c_797]) ).

tcf(c_164008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150344,c_796]) ).

tcf(c_164009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150344,c_642]) ).

tcf(c_164010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150344,c_774]) ).

tcf(c_164011,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_150344,c_770]) ).

tcf(c_164012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_150344,c_768]) ).

tcf(c_164013,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150344,c_763]) ).

tcf(c_164052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150352,c_144852]) ).

tcf(c_164053,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150352,c_125973]) ).

tcf(c_164054,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150352,c_125887]) ).

tcf(c_164055,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150352,c_633]) ).

tcf(c_164056,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_150352,c_776]) ).

tcf(c_164057,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150352,c_762]) ).

tcf(c_164058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150352,c_761]) ).

tcf(c_164059,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150352,c_797]) ).

tcf(c_164063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150352,c_796]) ).

tcf(c_164064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150352,c_642]) ).

tcf(c_164065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150352,c_774]) ).

tcf(c_164066,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_150352,c_770]) ).

tcf(c_164067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_150352,c_768]) ).

tcf(c_164068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150352,c_763]) ).

tcf(c_164338,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150357,c_144852]) ).

tcf(c_164339,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150357,c_125973]) ).

tcf(c_164340,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6),X0)),
    inference(superposition,[status(thm)],[c_150357,c_125887]) ).

tcf(c_164341,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150357,c_633]) ).

tcf(c_164342,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X2)),X3),X4),X5),X6),X7),X2),X2) ),
    inference(superposition,[status(thm)],[c_150357,c_776]) ).

tcf(c_164343,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150357,c_762]) ).

tcf(c_164344,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X1,X0,X3)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X2,X3,X3)),X4),X5),X6),X7),X8),X3) ),
    inference(superposition,[status(thm)],[c_150357,c_761]) ).

tcf(c_164345,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X3,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X3,X0,X2,X2)),X4),X5),X6),X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150357,c_797]) ).

tcf(c_164349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X2)),X3),X4),X5),X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150357,c_796]) ).

tcf(c_164350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X4 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X4,X2,X3)),X5),X6),X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150357,c_642]) ).

tcf(c_164351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X3,X2,X4)),X5),X6),X7),X8),X9),X1,X2,X4),X4)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150357,c_774]) ).

tcf(c_164352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X3,X2),X3),
    inference(superposition,[status(thm)],[c_150357,c_770]) ).

tcf(c_164353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X4),X5),X6),X7),X8),X2,X3),X2),
    inference(superposition,[status(thm)],[c_150357,c_768]) ).

tcf(c_164354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X0,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(hAPP(iPr_def_14,X0),X1),X2),X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150357,c_763]) ).

tcf(c_164379,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150961,c_562]) ).

tcf(c_164380,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150961,c_561]) ).

tcf(c_164381,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150961,c_565]) ).

tcf(c_164382,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_150961,c_144852]) ).

tcf(c_164383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150961,c_125973]) ).

tcf(c_164384,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150961,c_125887]) ).

tcf(c_164385,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150961,c_633]) ).

tcf(c_164386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150961,c_776]) ).

tcf(c_164387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_150961,c_762]) ).

tcf(c_164393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150961,c_796]) ).

tcf(c_164394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150961,c_642]) ).

tcf(c_164395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150961,c_774]) ).

tcf(c_164396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_150961,c_770]) ).

tcf(c_164397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_150961,c_768]) ).

tcf(c_164398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150961,c_763]) ).

tcf(c_164418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164394,c_150961]) ).

tcf(c_164421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164385,c_150961]) ).

tcf(c_164426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150972,c_562]) ).

tcf(c_164427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150972,c_561]) ).

tcf(c_164428,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150972,c_565]) ).

tcf(c_164429,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_150972,c_144852]) ).

tcf(c_164430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150972,c_125973]) ).

tcf(c_164431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150972,c_125887]) ).

tcf(c_164432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150972,c_633]) ).

tcf(c_164433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150972,c_776]) ).

tcf(c_164434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_150972,c_762]) ).

tcf(c_164440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150972,c_796]) ).

tcf(c_164441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150972,c_642]) ).

tcf(c_164442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6,X7),X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150972,c_774]) ).

tcf(c_164443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_150972,c_770]) ).

tcf(c_164444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X4),X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_150972,c_768]) ).

tcf(c_164445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150972,c_763]) ).

tcf(c_164465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2,X3),X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164441,c_150972]) ).

tcf(c_164468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5,X6),X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164432,c_150972]) ).

tcf(c_164469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X3,X4),X5),X6),X7),
    inference(superposition,[status(thm)],[c_150974,c_144852]) ).

tcf(c_164470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_150974,c_125973]) ).

tcf(c_164471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X6),X1)),
    inference(superposition,[status(thm)],[c_150974,c_125887]) ).

tcf(c_164472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150974,c_633]) ).

tcf(c_164473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X5,X6),X7),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X5,X6),X7),X3),X3) ),
    inference(superposition,[status(thm)],[c_150974,c_776]) ).

tcf(c_164474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X6,X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_150974,c_762]) ).

tcf(c_164475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X6,X7),X8),X4) ),
    inference(superposition,[status(thm)],[c_150974,c_761]) ).

tcf(c_164476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X6,X7),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150974,c_797]) ).

tcf(c_164480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(hAPP(c_fequal(X3),c_Pair(c_Pair(X0,X1,X2,X2),X4,X5,X6)),X5,X6),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150974,c_796]) ).

tcf(c_164481,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150974,c_642]) ).

tcf(c_164482,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,X7,X8)),X7,X8),X9),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150974,c_774]) ).

tcf(c_164483,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,X6,X7)),X6,X7),X8),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_150974,c_770]) ).

tcf(c_164484,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,X6,X7)),X6,X7),X8),X3,X4),X3),
    inference(superposition,[status(thm)],[c_150974,c_768]) ).

tcf(c_164485,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150974,c_763]) ).

tcf(c_164509,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150984,c_562]) ).

tcf(c_164510,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150984,c_561]) ).

tcf(c_164511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150984,c_565]) ).

tcf(c_164512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_150984,c_144852]) ).

tcf(c_164513,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150984,c_125973]) ).

tcf(c_164514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150984,c_125887]) ).

tcf(c_164515,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150984,c_633]) ).

tcf(c_164516,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150984,c_776]) ).

tcf(c_164517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_150984,c_762]) ).

tcf(c_164523,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150984,c_796]) ).

tcf(c_164524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150984,c_642]) ).

tcf(c_164525,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150984,c_774]) ).

tcf(c_164526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_150984,c_770]) ).

tcf(c_164527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_150984,c_768]) ).

tcf(c_164528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150984,c_763]) ).

tcf(c_164548,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164524,c_150984]) ).

tcf(c_164551,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164515,c_150984]) ).

tcf(c_164661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3,X3),X4),X5),
    inference(superposition,[status(thm)],[c_743,c_150996]) ).

tcf(c_164666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150996,c_562]) ).

tcf(c_164667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_150996,c_561]) ).

tcf(c_164668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150996,c_565]) ).

tcf(c_164669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_150996,c_144852]) ).

tcf(c_164670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150996,c_125973]) ).

tcf(c_164671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_150996,c_125887]) ).

tcf(c_164672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_150996,c_633]) ).

tcf(c_164673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_150996,c_776]) ).

tcf(c_164674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_150996,c_762]) ).

tcf(c_164680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_150996,c_796]) ).

tcf(c_164681,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_150996,c_642]) ).

tcf(c_164682,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_150996,c_774]) ).

tcf(c_164683,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_150996,c_770]) ).

tcf(c_164684,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_150996,c_768]) ).

tcf(c_164685,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_150996,c_763]) ).

tcf(c_164705,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164681,c_150996]) ).

tcf(c_164708,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164672,c_150996]) ).

tcf(c_164715,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151010,c_562]) ).

tcf(c_164716,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151010,c_561]) ).

tcf(c_164717,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_151010,c_565]) ).

tcf(c_164718,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_151010,c_144852]) ).

tcf(c_164719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_151010,c_125973]) ).

tcf(c_164720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_151010,c_125887]) ).

tcf(c_164721,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151010,c_633]) ).

tcf(c_164722,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_151010,c_776]) ).

tcf(c_164723,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_151010,c_762]) ).

tcf(c_164729,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_151010,c_796]) ).

tcf(c_164730,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151010,c_642]) ).

tcf(c_164731,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151010,c_774]) ).

tcf(c_164732,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_151010,c_770]) ).

tcf(c_164733,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_151010,c_768]) ).

tcf(c_164734,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_151010,c_763]) ).

tcf(c_164754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164730,c_151010]) ).

tcf(c_164757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164721,c_151010]) ).

tcf(c_164776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151352,c_562]) ).

tcf(c_164777,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151352,c_561]) ).

tcf(c_164778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_151352,c_565]) ).

tcf(c_164779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X8),
    inference(superposition,[status(thm)],[c_151352,c_144852]) ).

tcf(c_164780,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_151352,c_125973]) ).

tcf(c_164781,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6),X7)),
    inference(superposition,[status(thm)],[c_151352,c_125887]) ).

tcf(c_164782,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151352,c_633]) ).

tcf(c_164783,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_151352,c_776]) ).

tcf(c_164784,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7) ),
    inference(superposition,[status(thm)],[c_151352,c_762]) ).

tcf(c_164790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_151352,c_796]) ).

tcf(c_164791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151352,c_642]) ).

tcf(c_164792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7,X8),X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151352,c_774]) ).

tcf(c_164793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_151352,c_770]) ).

tcf(c_164794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X5),X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_151352,c_768]) ).

tcf(c_164795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_151352,c_763]) ).

tcf(c_164815,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3,X4),X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164791,c_151352]) ).

tcf(c_164818,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6,X7),X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164782,c_151352]) ).

tcf(c_164913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_687,c_151368]) ).

tcf(c_164914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_698,c_151368]) ).

tcf(c_164919,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151368,c_562]) ).

tcf(c_164920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151368,c_561]) ).

tcf(c_164921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151368,c_565]) ).

tcf(c_164922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_151368,c_144852]) ).

tcf(c_164923,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_151368,c_125973]) ).

tcf(c_164924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_151368,c_125887]) ).

tcf(c_164925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151368,c_633]) ).

tcf(c_164926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151368,c_776]) ).

tcf(c_164927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_151368,c_762]) ).

tcf(c_164933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_151368,c_796]) ).

tcf(c_164934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151368,c_642]) ).

tcf(c_164935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151368,c_774]) ).

tcf(c_164936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_151368,c_770]) ).

tcf(c_164937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_151368,c_768]) ).

tcf(c_164938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_151368,c_763]) ).

tcf(c_164958,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164934,c_151368]) ).

tcf(c_164961,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164925,c_151368]) ).

tcf(c_164969,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X3),X4),
    inference(demodulation,[status(thm)],[c_164914,c_596]) ).

tcf(c_164970,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2),X2,X2),X3),X4),
    inference(superposition,[status(thm)],[c_596,c_151397]) ).

tcf(c_164976,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151397,c_562]) ).

tcf(c_164977,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151397,c_561]) ).

tcf(c_164978,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151397,c_565]) ).

tcf(c_164979,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X6),
    inference(superposition,[status(thm)],[c_151397,c_144852]) ).

tcf(c_164980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_151397,c_125973]) ).

tcf(c_164981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4),X5)),
    inference(superposition,[status(thm)],[c_151397,c_125887]) ).

tcf(c_164982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151397,c_633]) ).

tcf(c_164983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151397,c_776]) ).

tcf(c_164984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5) ),
    inference(superposition,[status(thm)],[c_151397,c_762]) ).

tcf(c_164990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(superposition,[status(thm)],[c_151397,c_796]) ).

tcf(c_164991,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151397,c_642]) ).

tcf(c_164992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X5,X5),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151397,c_774]) ).

tcf(c_164993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_151397,c_770]) ).

tcf(c_164994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2,X2),X4),X5,X6),X5),
    inference(superposition,[status(thm)],[c_151397,c_768]) ).

tcf(c_164995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_151397,c_763]) ).

tcf(c_165015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X1,X1),X3),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164991,c_151397]) ).

tcf(c_165018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X4,X4),X6),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_164982,c_151397]) ).

tcf(c_165108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151447,c_560]) ).

tcf(c_165109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151447,c_564]) ).

tcf(c_165110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151447,c_562]) ).

tcf(c_165111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151447,c_561]) ).

tcf(c_165112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X6))
      | hBOOL(hAPP(X7,X0))
      | c_in(c_Pair(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X7,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5,X5),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151447,c_565]) ).

tcf(c_165113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_151447,c_144852]) ).

tcf(c_165114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_151447,c_125973]) ).

tcf(c_165115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_151447,c_125887]) ).

tcf(c_165116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151447,c_633]) ).

tcf(c_165117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X5,X5),X1,X2)
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151447,c_776]) ).

tcf(c_165118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_151447,c_762]) ).

tcf(c_165119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X6,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_151447,c_761]) ).

tcf(c_165120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151447,c_797]) ).

tcf(c_165124,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151447,c_796]) ).

tcf(c_165125,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X3),X4,X5)
      | ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151447,c_642]) ).

tcf(c_165126,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X3,X2,X8),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151447,c_774]) ).

tcf(c_165127,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X6,X5),X6) ),
    inference(superposition,[status(thm)],[c_151447,c_770]) ).

tcf(c_165128,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X5) ),
    inference(superposition,[status(thm)],[c_151447,c_768]) ).

tcf(c_165129,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X1)
      | c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_151447,c_763]) ).

tcf(c_165303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151736,c_560]) ).

tcf(c_165304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151736,c_564]) ).

tcf(c_165305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151736,c_562]) ).

tcf(c_165306,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | c_in(c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_151736,c_561]) ).

tcf(c_165307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X6))
      | hBOOL(hAPP(X7,X0))
      | c_in(c_Pair(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X7,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5,X5),X1,X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151736,c_565]) ).

tcf(c_165308,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,X1,X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_151736,c_144852]) ).

tcf(c_165309,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_151736,c_125973]) ).

tcf(c_165310,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_151736,c_125887]) ).

tcf(c_165311,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151736,c_633]) ).

tcf(c_165312,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X5,X5),X1,X2)
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_151736,c_776]) ).

tcf(c_165313,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_151736,c_762]) ).

tcf(c_165314,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X6,X0,X5)
      | c_in(c_Pair(X6,X7,X5,X5),X1,X2)
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_151736,c_761]) ).

tcf(c_165315,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X0,X2,X2),X3,X4)
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151736,c_797]) ).

tcf(c_165319,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),X3,X4)
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_151736,c_796]) ).

tcf(c_165320,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X8,X2,X3),X4,X5)
      | ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_151736,c_642]) ).

tcf(c_165321,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X3,X2,X8),X4,X5)
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_151736,c_774]) ).

tcf(c_165322,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X0,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X6,X5),X6) ),
    inference(superposition,[status(thm)],[c_151736,c_770]) ).

tcf(c_165323,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X0,X7,X5,X6),X1,X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X5) ),
    inference(superposition,[status(thm)],[c_151736,c_768]) ).

tcf(c_165324,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X1)
      | c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_151736,c_763]) ).

tcf(c_165411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X3)),X3,X3),X4),
    inference(superposition,[status(thm)],[c_743,c_159951]) ).

tcf(c_165412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X3,X4),X6),X7),
    inference(superposition,[status(thm)],[c_159951,c_144852]) ).

tcf(c_165413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6),X1)),
    inference(superposition,[status(thm)],[c_159951,c_125973]) ).

tcf(c_165414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6),X1)),
    inference(superposition,[status(thm)],[c_159951,c_125887]) ).

tcf(c_165415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X8),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X8),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_159951,c_633]) ).

tcf(c_165416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X7),X5,X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X7),X5,X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_159951,c_776]) ).

tcf(c_165417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X8),X6,X7),X4) ),
    inference(superposition,[status(thm)],[c_159951,c_762]) ).

tcf(c_165418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X8),X6,X7),X4) ),
    inference(superposition,[status(thm)],[c_159951,c_761]) ).

tcf(c_165419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X9),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X9),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_159951,c_642]) ).

tcf(c_165420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,X7,X8)),X9),X7,X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_159951,c_774]) ).

tcf(c_165421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,X6,X7)),X8),X6,X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_159951,c_770]) ).

tcf(c_165422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,X6,X7)),X8),X6,X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_159951,c_768]) ).

tcf(c_165423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6,X7) ),
    inference(superposition,[status(thm)],[c_159951,c_763]) ).

tcf(c_165624,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(X0,X2,X3,X4)),X5),X3,X4),X6),X7),
    inference(superposition,[status(thm)],[c_159952,c_144852]) ).

tcf(c_165625,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6),X1)),
    inference(superposition,[status(thm)],[c_159952,c_125973]) ).

tcf(c_165626,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6),X1)),
    inference(superposition,[status(thm)],[c_159952,c_125887]) ).

tcf(c_165627,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X8),X6,X7),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X3),c_Pair(c_Pair(X4,X0,X2,X2),X5,X6,X7)),X8),X6,X7),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_159952,c_633]) ).

tcf(c_165628,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X7),X5,X6),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X3),X4,X5,X6)),X7),X5,X6),X3),X3) ),
    inference(superposition,[status(thm)],[c_159952,c_776]) ).

tcf(c_165629,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X8),X6,X7),X4) ),
    inference(superposition,[status(thm)],[c_159952,c_762]) ).

tcf(c_165630,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X3,X4,X4),X5,X6,X7)),X8),X6,X7),X4) ),
    inference(superposition,[status(thm)],[c_159952,c_761]) ).

tcf(c_165631,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X9),X7,X8),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X5,X2,X3),X6,X7,X8)),X9),X7,X8),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_159952,c_642]) ).

tcf(c_165632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X4),c_Pair(c_Pair(X0,X3,X2,X5),X6,X7,X8)),X9),X7,X8),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_159952,c_774]) ).

tcf(c_165633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X2,X0,X3,X4),X5,X6,X7)),X8),X6,X7),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_159952,c_770]) ).

tcf(c_165634,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X1),c_Pair(c_Pair(X0,X2,X3,X4),X5,X6,X7)),X8),X6,X7),X3,X4),X3),
    inference(superposition,[status(thm)],[c_159952,c_768]) ).

tcf(c_165635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X1,X1,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(hAPP(c_fequal(X0),c_Pair(X1,X2,X3,X4)),X5),X3,X4),X6,X7) ),
    inference(superposition,[status(thm)],[c_159952,c_763]) ).

tcf(c_165741,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_159958,c_562]) ).

tcf(c_165742,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_159958,c_561]) ).

tcf(c_165743,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_159958,c_565]) ).

tcf(c_165744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_159958,c_144852]) ).

tcf(c_165745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_159958,c_125973]) ).

tcf(c_165746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_159958,c_125887]) ).

tcf(c_165747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_159958,c_633]) ).

tcf(c_165748,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_159958,c_776]) ).

tcf(c_165749,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_159958,c_762]) ).

tcf(c_165751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_159958,c_642]) ).

tcf(c_165752,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_159958,c_774]) ).

tcf(c_165753,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_159958,c_770]) ).

tcf(c_165754,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_159958,c_768]) ).

tcf(c_165755,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_159958,c_763]) ).

tcf(c_165775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_165751,c_159958]) ).

tcf(c_165778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_165747,c_159958]) ).

tcf(c_165779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X4),X5),
    inference(superposition,[status(thm)],[c_743,c_160217]) ).

tcf(c_165785,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160217,c_562]) ).

tcf(c_165786,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160217,c_561]) ).

tcf(c_165787,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160217,c_565]) ).

tcf(c_165788,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160217,c_144852]) ).

tcf(c_165789,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160217,c_125973]) ).

tcf(c_165790,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160217,c_125887]) ).

tcf(c_165791,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160217,c_633]) ).

tcf(c_165792,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160217,c_776]) ).

tcf(c_165793,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160217,c_762]) ).

tcf(c_165795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160217,c_642]) ).

tcf(c_165796,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160217,c_774]) ).

tcf(c_165797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160217,c_770]) ).

tcf(c_165798,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160217,c_768]) ).

tcf(c_165799,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160217,c_763]) ).

tcf(c_165819,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_165795,c_160217]) ).

tcf(c_165822,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_165791,c_160217]) ).

tcf(c_165828,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160223,c_562]) ).

tcf(c_165829,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160223,c_561]) ).

tcf(c_165830,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160223,c_565]) ).

tcf(c_165831,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160223,c_144852]) ).

tcf(c_165832,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160223,c_125973]) ).

tcf(c_165833,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160223,c_125887]) ).

tcf(c_165834,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160223,c_633]) ).

tcf(c_165835,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160223,c_776]) ).

tcf(c_165836,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160223,c_762]) ).

tcf(c_165838,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160223,c_642]) ).

tcf(c_165839,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160223,c_774]) ).

tcf(c_165840,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160223,c_770]) ).

tcf(c_165841,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160223,c_768]) ).

tcf(c_165842,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160223,c_763]) ).

tcf(c_165862,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_165838,c_160223]) ).

tcf(c_165865,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_165834,c_160223]) ).

tcf(c_165895,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4,X4),X5),
    inference(superposition,[status(thm)],[c_743,c_160229]) ).

tcf(c_165900,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160229,c_562]) ).

tcf(c_165901,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160229,c_561]) ).

tcf(c_165902,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160229,c_565]) ).

tcf(c_165903,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160229,c_144852]) ).

tcf(c_165904,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160229,c_125973]) ).

tcf(c_165905,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160229,c_125887]) ).

tcf(c_165906,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160229,c_633]) ).

tcf(c_165907,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160229,c_776]) ).

tcf(c_165908,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160229,c_762]) ).

tcf(c_165910,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160229,c_642]) ).

tcf(c_165911,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X6),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160229,c_774]) ).

tcf(c_165912,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160229,c_770]) ).

tcf(c_165913,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X3),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160229,c_768]) ).

tcf(c_165914,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160229,c_763]) ).

tcf(c_165934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X2),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_165910,c_160229]) ).

tcf(c_165937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X3,X4),X4,X4),X5),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_165906,c_160229]) ).

tcf(c_165946,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_OId__on(X0,X1),X2,X1),X0,X3) ),
    inference(superposition,[status(thm)],[c_724,c_160236]) ).

tcf(c_165947,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X3) ),
    inference(superposition,[status(thm)],[c_743,c_160236]) ).

tcf(c_165948,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,X2,X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_160236,c_144852]) ).

tcf(c_165949,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,X1,X1),X2),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X1))) ),
    inference(superposition,[status(thm)],[c_160236,c_125973]) ).

tcf(c_165950,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(X0,X1,X1),X2),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X1))) ),
    inference(superposition,[status(thm)],[c_160236,c_125887]) ).

tcf(c_165951,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(X0,X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X4,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X4,X1),X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(X0,X1,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_160236,c_763]) ).

tcf(c_165980,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_OId__on(X0,X1),X2,X1),X0,X3) ),
    inference(superposition,[status(thm)],[c_724,c_160421]) ).

tcf(c_165981,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X0,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Transitive__Closure_Otrancl(X0,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X3) ),
    inference(superposition,[status(thm)],[c_743,c_160421]) ).

tcf(c_165982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,X2,X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_160421,c_144852]) ).

tcf(c_165983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X0,X1,X1),X2),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X1))) ),
    inference(superposition,[status(thm)],[c_160421,c_125973]) ).

tcf(c_165984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(X0,X1,X1),X2),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X1))) ),
    inference(superposition,[status(thm)],[c_160421,c_125887]) ).

tcf(c_165985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(X0,X1),X1)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X4,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X4,X1),X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(X0,X1,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_160421,c_763]) ).

tcf(c_166021,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160434,c_562]) ).

tcf(c_166022,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160434,c_561]) ).

tcf(c_166023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160434,c_565]) ).

tcf(c_166024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160434,c_144852]) ).

tcf(c_166025,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160434,c_125973]) ).

tcf(c_166026,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160434,c_125887]) ).

tcf(c_166027,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160434,c_633]) ).

tcf(c_166028,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160434,c_776]) ).

tcf(c_166029,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160434,c_762]) ).

tcf(c_166031,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160434,c_642]) ).

tcf(c_166032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160434,c_774]) ).

tcf(c_166033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160434,c_770]) ).

tcf(c_166034,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160434,c_768]) ).

tcf(c_166035,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160434,c_763]) ).

tcf(c_166055,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166031,c_160434]) ).

tcf(c_166058,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166027,c_160434]) ).

tcf(c_166098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X4),X5),
    inference(superposition,[status(thm)],[c_743,c_160442]) ).

tcf(c_166105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160442,c_562]) ).

tcf(c_166106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160442,c_561]) ).

tcf(c_166107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160442,c_565]) ).

tcf(c_166108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160442,c_144852]) ).

tcf(c_166109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160442,c_125973]) ).

tcf(c_166110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160442,c_125887]) ).

tcf(c_166111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160442,c_633]) ).

tcf(c_166112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160442,c_776]) ).

tcf(c_166113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160442,c_762]) ).

tcf(c_166115,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160442,c_642]) ).

tcf(c_166116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160442,c_774]) ).

tcf(c_166117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160442,c_770]) ).

tcf(c_166118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160442,c_768]) ).

tcf(c_166119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160442,c_763]) ).

tcf(c_166139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166115,c_160442]) ).

tcf(c_166142,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166111,c_160442]) ).

tcf(c_166349,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160448,c_562]) ).

tcf(c_166350,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160448,c_561]) ).

tcf(c_166351,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160448,c_565]) ).

tcf(c_166352,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160448,c_144852]) ).

tcf(c_166353,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160448,c_125973]) ).

tcf(c_166354,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160448,c_125887]) ).

tcf(c_166355,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160448,c_633]) ).

tcf(c_166356,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160448,c_776]) ).

tcf(c_166357,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160448,c_762]) ).

tcf(c_166359,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160448,c_642]) ).

tcf(c_166360,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160448,c_774]) ).

tcf(c_166361,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160448,c_770]) ).

tcf(c_166362,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160448,c_768]) ).

tcf(c_166363,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160448,c_763]) ).

tcf(c_166383,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166359,c_160448]) ).

tcf(c_166386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166355,c_160448]) ).

tcf(c_166387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4,X4),X5),
    inference(superposition,[status(thm)],[c_743,c_160455]) ).

tcf(c_166393,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160455,c_562]) ).

tcf(c_166394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160455,c_561]) ).

tcf(c_166395,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160455,c_565]) ).

tcf(c_166396,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160455,c_144852]) ).

tcf(c_166397,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160455,c_125973]) ).

tcf(c_166398,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160455,c_125887]) ).

tcf(c_166399,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160455,c_633]) ).

tcf(c_166400,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160455,c_776]) ).

tcf(c_166401,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160455,c_762]) ).

tcf(c_166403,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160455,c_642]) ).

tcf(c_166404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X5,X5),X7),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160455,c_774]) ).

tcf(c_166405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160455,c_770]) ).

tcf(c_166406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X4),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160455,c_768]) ).

tcf(c_166407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160455,c_763]) ).

tcf(c_166427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X1,X1),X3),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166403,c_160455]) ).

tcf(c_166430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X4,X4),X6),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166399,c_160455]) ).

tcf(c_166465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160462,c_562]) ).

tcf(c_166466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160462,c_561]) ).

tcf(c_166467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160462,c_565]) ).

tcf(c_166468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160462,c_144852]) ).

tcf(c_166469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160462,c_125973]) ).

tcf(c_166470,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160462,c_125887]) ).

tcf(c_166471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160462,c_633]) ).

tcf(c_166472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160462,c_776]) ).

tcf(c_166473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160462,c_762]) ).

tcf(c_166475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160462,c_642]) ).

tcf(c_166476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160462,c_774]) ).

tcf(c_166477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160462,c_770]) ).

tcf(c_166478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160462,c_768]) ).

tcf(c_166479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160462,c_763]) ).

tcf(c_166499,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166475,c_160462]) ).

tcf(c_166502,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166471,c_160462]) ).

tcf(c_166524,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160874,c_562]) ).

tcf(c_166525,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_160874,c_561]) ).

tcf(c_166526,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160874,c_565]) ).

tcf(c_166527,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_160874,c_144852]) ).

tcf(c_166528,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160874,c_125973]) ).

tcf(c_166529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_160874,c_125887]) ).

tcf(c_166530,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_160874,c_633]) ).

tcf(c_166531,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_160874,c_776]) ).

tcf(c_166532,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_160874,c_762]) ).

tcf(c_166534,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_160874,c_642]) ).

tcf(c_166535,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_160874,c_774]) ).

tcf(c_166536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_160874,c_770]) ).

tcf(c_166537,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_160874,c_768]) ).

tcf(c_166538,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_160874,c_763]) ).

tcf(c_166558,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166534,c_160874]) ).

tcf(c_166561,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166530,c_160874]) ).

tcf(c_166583,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161271,c_562]) ).

tcf(c_166584,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161271,c_561]) ).

tcf(c_166585,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_161271,c_565]) ).

tcf(c_166586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_161271,c_144852]) ).

tcf(c_166587,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_161271,c_125973]) ).

tcf(c_166588,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_161271,c_125887]) ).

tcf(c_166589,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161271,c_633]) ).

tcf(c_166590,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_161271,c_776]) ).

tcf(c_166591,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_161271,c_762]) ).

tcf(c_166593,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161271,c_642]) ).

tcf(c_166594,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161271,c_774]) ).

tcf(c_166595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_161271,c_770]) ).

tcf(c_166596,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_161271,c_768]) ).

tcf(c_166597,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_161271,c_763]) ).

tcf(c_166617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166593,c_161271]) ).

tcf(c_166620,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166589,c_161271]) ).

tcf(c_166658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X8,X0))
      | c_in(X7,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161527,c_562]) ).

tcf(c_166659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X7,X8))
      | hBOOL(hAPP(X7,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161527,c_561]) ).

tcf(c_166660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(X8,X9))
      | hBOOL(hAPP(X8,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_161527,c_565]) ).

tcf(c_166661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X8),
    inference(superposition,[status(thm)],[c_161527,c_144852]) ).

tcf(c_166662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_161527,c_125973]) ).

tcf(c_166663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6),X7)),
    inference(superposition,[status(thm)],[c_161527,c_125887]) ).

tcf(c_166664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(X9,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161527,c_633]) ).

tcf(c_166665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7),X7) ),
    inference(superposition,[status(thm)],[c_161527,c_776]) ).

tcf(c_166666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X8,X0,X7)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7) ),
    inference(superposition,[status(thm)],[c_161527,c_762]) ).

tcf(c_166668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X1 = X10 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161527,c_642]) ).

tcf(c_166669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X8,X9),X1,X2,X10),X10)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161527,c_774]) ).

tcf(c_166670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X8,X7),X8),
    inference(superposition,[status(thm)],[c_161527,c_770]) ).

tcf(c_166671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X5,X6),X7,X8),X7),
    inference(superposition,[status(thm)],[c_161527,c_768]) ).

tcf(c_166672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X8,X8,X7,X7),X6,tc_prod(X7,X7))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(superposition,[status(thm)],[c_161527,c_763]) ).

tcf(c_166692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( ( X8 = X9 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X4,X5),X6,X7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_166668,c_161527]) ).

tcf(c_166695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X7,X8),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_166664,c_161527]) ).

tcf(c_166715,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_596,c_161650]) ).

tcf(c_166716,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X1,X2),X0))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_670,c_161650]) ).

tcf(c_166717,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X0))
      | c_in(X0,c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_684,c_161650]) ).

tcf(c_166718,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_687,c_161650]) ).

tcf(c_166719,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X2,X3,X3),X3),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Wellfounded_Oacc(c_Relation_Oconverse(X2,X3,X3),X3),X1),c_Relation_ODomain(X2,X3,X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161650,c_517]) ).

tcf(c_166720,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),X1,X2),c_Relation_ODomain(X3,X4,X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_161650,c_537]) ).

tcf(c_166721,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,X2,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_161650,c_841]) ).

tcf(c_166728,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,X1,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X2)) ),
    inference(light_normalisation,[status(thm)],[c_166718,c_743]) ).

tcf(c_166756,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_161801]) ).

tcf(c_166759,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_161801]) ).

tcf(c_166760,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_Oconverse(X0,X1,X1),X2,X1))) ),
    inference(superposition,[status(thm)],[c_161801,c_511]) ).

tcf(c_166761,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(c_Relation_ODomain(X1,t_a,t_a),X2))
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_Oconverse(X1,t_a,t_a)))) ),
    inference(superposition,[status(thm)],[c_161801,c_553]) ).

tcf(c_166762,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_Oconverse(X0,X1,X1),X2,X1))) ),
    inference(superposition,[status(thm)],[c_161801,c_545]) ).

tcf(c_166763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(c_Relation_ODomain(X1,X2,X2),X3))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_Oconverse(X1,X2,X2),X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_161801,c_550]) ).

tcf(c_166764,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161801,c_560]) ).

tcf(c_166765,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161801,c_564]) ).

tcf(c_166766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161801,c_562]) ).

tcf(c_166767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161801,c_561]) ).

tcf(c_166768,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161801,c_565]) ).

tcf(c_166769,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_161801,c_144852]) ).

tcf(c_166770,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X2))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_161801,c_125973]) ).

tcf(c_166771,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X2))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_161801,c_125887]) ).

tcf(c_166772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X3,tc_prod(X2,X2),tc_prod(X2,X2)),c_Pair(X4,X0,X2,X2)))
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161801,c_633]) ).

tcf(c_166773,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),c_Pair(X3,X0,X2,X2)))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_161801,c_776]) ).

tcf(c_166774,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),c_Pair(X3,X4,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_161801,c_762]) ).

tcf(c_166775,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X2)
      | hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),c_Pair(X3,X4,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_161801,c_761]) ).

tcf(c_166776,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X4,tc_prod(X2,X3),tc_prod(X2,X3)),c_Pair(X0,X5,X2,X3)))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161801,c_642]) ).

tcf(c_166777,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X4,tc_prod(X2,X5),tc_prod(X2,X5)),c_Pair(X0,X3,X2,X5)))
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161801,c_774]) ).

tcf(c_166778,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X3),tc_prod(X2,X3)),c_Pair(X4,X0,X2,X3)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_161801,c_770]) ).

tcf(c_166779,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,tc_prod(X2,X3),tc_prod(X2,X3)),c_Pair(X0,X4,X2,X3)))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_161801,c_768]) ).

tcf(c_166780,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X3))
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_161801,c_763]) ).

tcf(c_166781,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_161801,c_840]) ).

tcf(c_166782,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,iPr_def_13,iPr_def_13),c_Pair(X0,X2,iPr_def_11,iPr_def_12)))
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,iPr_def_13,iPr_def_13),iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_161801,c_126501]) ).

tcf(c_166920,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_596,c_161806]) ).

tcf(c_166921,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,X2,X2),X3)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_670,c_161806]) ).

tcf(c_166922,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_684,c_161806]) ).

tcf(c_166923,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X1,X2),X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_687,c_161806]) ).

tcf(c_166924,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2)),t_a,t_a),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161806,c_560]) ).

tcf(c_166925,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2)),t_a,t_a),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161806,c_564]) ).

tcf(c_166926,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2)),t_a,t_a),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161806,c_562]) ).

tcf(c_166927,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2)),t_a,t_a),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_161806,c_561]) ).

tcf(c_166928,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3),X3,X3),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_161806,c_565]) ).

tcf(c_166929,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_161806,c_144852]) ).

tcf(c_166930,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_161806,c_125973]) ).

tcf(c_166931,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_161806,c_125887]) ).

tcf(c_166932,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),c_Wellfounded_Oacc(X3,X4),X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(X3,X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(X3,X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_161806,c_633]) ).

tcf(c_166933,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X0,X3,X3),c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_161806,c_776]) ).

tcf(c_166934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_161806,c_762]) ).

tcf(c_166935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),c_Wellfounded_Oacc(X1,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_161806,c_761]) ).

tcf(c_166936,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X3),c_Wellfounded_Oacc(X4,X5),X5)
      | ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(X4,X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(X4,X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_161806,c_642]) ).

tcf(c_166937,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X6),c_Wellfounded_Oacc(X4,X5),X5)
      | c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(X4,X5,X5),X5,X5),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_161806,c_774]) ).

tcf(c_166938,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X3,X4),c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_161806,c_770]) ).

tcf(c_166939,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X3,X4),c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X3,X4),X3) ),
    inference(superposition,[status(thm)],[c_161806,c_768]) ).

tcf(c_166940,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(X0,X1),X1)
      | c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_161806,c_763]) ).

tcf(c_167097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,X0,X2,X3)),X2,X3),X3,X2),X4),X5),
    inference(superposition,[status(thm)],[c_162698,c_144852]) ).

tcf(c_167098,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X3,X2),X4),X1)),
    inference(superposition,[status(thm)],[c_162698,c_125973]) ).

tcf(c_167099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X3,X2),X4),X1)),
    inference(superposition,[status(thm)],[c_162698,c_125887]) ).

tcf(c_167100,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X3,c_Pair(X4,X0,X2,X2),X5,X6)),X5,X6),X6,X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X3,c_Pair(X4,X0,X2,X2),X5,X6)),X5,X6),X6,X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162698,c_633]) ).

tcf(c_167101,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X0,X3,X3),X4,X5)),X4,X5),X5,X4),X3),X3)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X0,X3,X3),X4,X5)),X4,X5),X5,X4),X3),X3) ),
    inference(superposition,[status(thm)],[c_162698,c_776]) ).

tcf(c_167102,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X3,X4,X4),X5,X6)),X5,X6),X6,X5),X4) ),
    inference(superposition,[status(thm)],[c_162698,c_762]) ).

tcf(c_167103,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X2,X0,X4)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X3,X4,X4),X5,X6)),X5,X6),X6,X5),X4) ),
    inference(superposition,[status(thm)],[c_162698,c_761]) ).

tcf(c_167104,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X4,c_Pair(X0,X5,X2,X3),X6,X7)),X6,X7),X7,X6),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X4,c_Pair(X0,X5,X2,X3),X6,X7)),X6,X7),X7,X6),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162698,c_642]) ).

tcf(c_167105,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X4,c_Pair(X0,X3,X2,X5),X6,X7)),X6,X7),X7,X6),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162698,c_774]) ).

tcf(c_167106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X2,X0,X3,X4),X5,X6)),X5,X6),X6,X5),X3,X4),X4,X3),X4),
    inference(superposition,[status(thm)],[c_162698,c_770]) ).

tcf(c_167107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X1,c_Pair(X0,X2,X3,X4),X5,X6)),X5,X6),X6,X5),X3,X4),X3),
    inference(superposition,[status(thm)],[c_162698,c_768]) ).

tcf(c_167108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X1,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(hAPP(iPr_def_14,c_Pair(X0,X1,X2,X3)),X2,X3),X3,X2),X4,X5) ),
    inference(superposition,[status(thm)],[c_162698,c_763]) ).

tcf(c_167143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162155,c_560]) ).

tcf(c_167144,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162155,c_564]) ).

tcf(c_167145,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162155,c_562]) ).

tcf(c_167146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162155,c_561]) ).

tcf(c_167147,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X6))
      | hBOOL(hAPP(X7,X0))
      | hBOOL(hAPP(X1,c_Pair(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X7,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5,X5)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_162155,c_565]) ).

tcf(c_167148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_162155,c_144852]) ).

tcf(c_167149,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_162155,c_125973]) ).

tcf(c_167150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_162155,c_125887]) ).

tcf(c_167151,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X6,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_793]) ).

tcf(c_167152,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162155,c_632]) ).

tcf(c_167153,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162155,c_631]) ).

tcf(c_167154,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_847]) ).

tcf(c_167155,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162155,c_799]) ).

tcf(c_167156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_798]) ).

tcf(c_167157,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162155,c_795]) ).

tcf(c_167158,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_849]) ).

tcf(c_167159,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X1,X6,X2,X2)))
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_848]) ).

tcf(c_167161,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X1,X6,X2,X2)))
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_781]) ).

tcf(c_167162,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_162155,c_794]) ).

tcf(c_167163,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_162155,c_784]) ).

tcf(c_167164,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162155,c_800]) ).

tcf(c_167165,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162155,c_786]) ).

tcf(c_167166,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X1,X2,X2)))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_162155,c_789]) ).

tcf(c_167168,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X2,c_Pair(X0,X1,X5,X5)))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_162155,c_806]) ).

tcf(c_167169,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X7,X0,X2,X2)))
      | c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162155,c_633]) ).

tcf(c_167170,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X6,X0,X5,X5)))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_162155,c_776]) ).

tcf(c_167171,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | hBOOL(hAPP(X1,c_Pair(X6,X7,X5,X5)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162155,c_762]) ).

tcf(c_167172,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X6,X0,X5)
      | hBOOL(hAPP(X1,c_Pair(X6,X7,X5,X5)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162155,c_761]) ).

tcf(c_167173,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X8,X2,X3)))
      | ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162155,c_642]) ).

tcf(c_167174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X3,X2,X8)))
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162155,c_774]) ).

tcf(c_167175,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X7,X0,X5,X6)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X6,X5),X6) ),
    inference(superposition,[status(thm)],[c_162155,c_770]) ).

tcf(c_167176,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X7,X5,X6)))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X5) ),
    inference(superposition,[status(thm)],[c_162155,c_768]) ).

tcf(c_167177,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_162155,c_763]) ).

tcf(c_167416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162156,c_517]) ).

tcf(c_167417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_162156,c_537]) ).

tcf(c_167430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162157,c_517]) ).

tcf(c_167431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_162157,c_537]) ).

tcf(c_167432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162157,c_841]) ).

tcf(c_167446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162571,c_560]) ).

tcf(c_167447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinduct__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162571,c_564]) ).

tcf(c_167448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a)
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162571,c_562]) ).

tcf(c_167449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X5))
      | hBOOL(hAPP(X6,X0))
      | hBOOL(hAPP(X1,c_Pair(X5,v_sko__Wellfounded__Xacc__Xinducts__1(X6,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4)),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162571,c_561]) ).

tcf(c_167450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X7,X6))
      | hBOOL(hAPP(X7,X0))
      | hBOOL(hAPP(X1,c_Pair(X6,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X7,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5,X5)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_162571,c_565]) ).

tcf(c_167451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X6) ),
    inference(superposition,[status(thm)],[c_162571,c_144852]) ).

tcf(c_167452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_162571,c_125973]) ).

tcf(c_167453,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4),X5)) ),
    inference(superposition,[status(thm)],[c_162571,c_125887]) ).

tcf(c_167454,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X6,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_793]) ).

tcf(c_167455,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162571,c_632]) ).

tcf(c_167456,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162571,c_631]) ).

tcf(c_167457,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_847]) ).

tcf(c_167458,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1,X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162571,c_799]) ).

tcf(c_167459,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_798]) ).

tcf(c_167460,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X5,X5),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),tc_prod(X5,X5))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162571,c_795]) ).

tcf(c_167461,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X6,X0,X2,X2)))
      | c_in(c_Pair(X6,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_849]) ).

tcf(c_167462,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X1,X6,X2,X2)))
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_848]) ).

tcf(c_167464,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X1,X6,X2,X2)))
      | c_in(c_Pair(X0,X6,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_781]) ).

tcf(c_167465,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_162571,c_794]) ).

tcf(c_167466,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5))) ),
    inference(superposition,[status(thm)],[c_162571,c_784]) ).

tcf(c_167467,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X6,X1,X5,X5)))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162571,c_800]) ).

tcf(c_167468,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | hBOOL(hAPP(X2,c_Pair(X1,X6,X5,X5)))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_162571,c_786]) ).

tcf(c_167469,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X0,X1,X2,X2)))
      | c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X2),tc_prod(X2,X2))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_162571,c_789]) ).

tcf(c_167471,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X2,c_Pair(X0,X1,X5,X5)))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5,X5),X5)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_162571,c_806]) ).

tcf(c_167472,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X3,c_Pair(X7,X0,X2,X2)))
      | c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162571,c_633]) ).

tcf(c_167473,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X6,X0,X5,X5)))
      | c_in(X6,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5),X5) ),
    inference(superposition,[status(thm)],[c_162571,c_776]) ).

tcf(c_167474,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X7,X0,X5)
      | hBOOL(hAPP(X1,c_Pair(X6,X7,X5,X5)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162571,c_762]) ).

tcf(c_167475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(X6,X0,X5)
      | hBOOL(hAPP(X1,c_Pair(X6,X7,X5,X5)))
      | ~ c_Relation_Orefl__on(X0,c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162571,c_761]) ).

tcf(c_167476,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X8,X2,X3)))
      | ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162571,c_642]) ).

tcf(c_167477,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(X4,c_Pair(X0,X3,X2,X8)))
      | c_in(X3,c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X6),X7),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162571,c_774]) ).

tcf(c_167478,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X7,X0,X5,X6)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X6,X5),X6) ),
    inference(superposition,[status(thm)],[c_162571,c_770]) ).

tcf(c_167479,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X1,c_Pair(X0,X7,X5,X6)))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5,X6),X5) ),
    inference(superposition,[status(thm)],[c_162571,c_768]) ).

tcf(c_167480,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X0,X6))
      | c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2),X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_162571,c_763]) ).

tcf(c_167695,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162572,c_517]) ).

tcf(c_167696,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_162572,c_537]) ).

tcf(c_167712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X0))
      | hBOOL(hAPP(X2,v_sko__Wellfounded__Xacc__Xinduct__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X4),X5),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162573,c_517]) ).

tcf(c_167713,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X0))
      | hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X5),X6),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_162573,c_537]) ).

tcf(c_167714,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X1,X0))
      | c_in(X0,c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3),X4),X5) ),
    inference(superposition,[status(thm)],[c_162573,c_841]) ).

tcf(c_167727,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X4),
    inference(superposition,[status(thm)],[c_687,c_162706]) ).

tcf(c_167733,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162706,c_562]) ).

tcf(c_167734,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162706,c_561]) ).

tcf(c_167735,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162706,c_565]) ).

tcf(c_167736,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_162706,c_144852]) ).

tcf(c_167737,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162706,c_125973]) ).

tcf(c_167738,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162706,c_125887]) ).

tcf(c_167739,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162706,c_633]) ).

tcf(c_167740,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162706,c_776]) ).

tcf(c_167741,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_162706,c_762]) ).

tcf(c_167743,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162706,c_642]) ).

tcf(c_167744,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162706,c_774]) ).

tcf(c_167745,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_162706,c_770]) ).

tcf(c_167746,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_162706,c_768]) ).

tcf(c_167747,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_162706,c_763]) ).

tcf(c_167767,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_167743,c_162706]) ).

tcf(c_167770,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_167739,c_162706]) ).

tcf(c_167975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X4),
    inference(superposition,[status(thm)],[c_596,c_162714]) ).

tcf(c_167982,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162714,c_562]) ).

tcf(c_167983,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162714,c_561]) ).

tcf(c_167984,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162714,c_565]) ).

tcf(c_167985,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_162714,c_144852]) ).

tcf(c_167986,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162714,c_125973]) ).

tcf(c_167987,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162714,c_125887]) ).

tcf(c_167988,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162714,c_633]) ).

tcf(c_167989,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162714,c_776]) ).

tcf(c_167990,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_162714,c_762]) ).

tcf(c_167992,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162714,c_642]) ).

tcf(c_167993,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162714,c_774]) ).

tcf(c_167994,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_162714,c_770]) ).

tcf(c_167995,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_162714,c_768]) ).

tcf(c_167996,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_162714,c_763]) ).

tcf(c_168016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_167992,c_162714]) ).

tcf(c_168019,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_167988,c_162714]) ).

tcf(c_168053,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X4),
    inference(superposition,[status(thm)],[c_596,c_162722]) ).

tcf(c_168060,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162722,c_562]) ).

tcf(c_168061,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162722,c_561]) ).

tcf(c_168062,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162722,c_565]) ).

tcf(c_168063,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_162722,c_144852]) ).

tcf(c_168064,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162722,c_125973]) ).

tcf(c_168065,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162722,c_125887]) ).

tcf(c_168066,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162722,c_633]) ).

tcf(c_168067,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162722,c_776]) ).

tcf(c_168068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_162722,c_762]) ).

tcf(c_168070,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162722,c_642]) ).

tcf(c_168071,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162722,c_774]) ).

tcf(c_168072,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_162722,c_770]) ).

tcf(c_168073,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_162722,c_768]) ).

tcf(c_168074,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_162722,c_763]) ).

tcf(c_168094,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_168070,c_162722]) ).

tcf(c_168097,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_168066,c_162722]) ).

tcf(c_168099,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X2,X2),X2),X2,X2),X4),
    inference(superposition,[status(thm)],[c_687,c_162731]) ).

tcf(c_168106,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X6,X0))
      | c_in(X5,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162731,c_562]) ).

tcf(c_168107,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(X5,X6))
      | hBOOL(hAPP(X5,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_162731,c_561]) ).

tcf(c_168108,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( hBOOL(hAPP(X6,X7))
      | hBOOL(hAPP(X6,X0))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162731,c_565]) ).

tcf(c_168109,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X6),
    inference(superposition,[status(thm)],[c_162731,c_144852]) ).

tcf(c_168110,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162731,c_125973]) ).

tcf(c_168111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4),X5)),
    inference(superposition,[status(thm)],[c_162731,c_125887]) ).

tcf(c_168112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_in(c_Pair(X7,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_162731,c_633]) ).

tcf(c_168113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5),X5) ),
    inference(superposition,[status(thm)],[c_162731,c_776]) ).

tcf(c_168114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,X0,X5)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5) ),
    inference(superposition,[status(thm)],[c_162731,c_762]) ).

tcf(c_168116,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( X1 = X8 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_162731,c_642]) ).

tcf(c_168117,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X4,X5),X6),X7),X5,X5),X5,X5),X1,X2,X8),X8)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_162731,c_774]) ).

tcf(c_168118,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X6,X5),X6),
    inference(superposition,[status(thm)],[c_162731,c_770]) ).

tcf(c_168119,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X3),X4),X2,X2),X2,X2),X5,X6),X5),
    inference(superposition,[status(thm)],[c_162731,c_768]) ).

tcf(c_168120,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X6,X6,X5,X5),X4,tc_prod(X5,X5))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(superposition,[status(thm)],[c_162731,c_763]) ).

tcf(c_168140,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ( X6 = X7 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X0,X1),X2),X3),X1,X1),X1,X1),X4,X5) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_168116,c_162731]) ).

tcf(c_168143,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X4),X5),X6),X4,X4),X4,X4),X2),tc_prod(X2,X2)),
    inference(forward_subsumption_resolution,[status(thm)],[c_168112,c_162731]) ).

tcf(c_168182,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(X1,X2),X2),X0))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_596,c_166716]) ).

tcf(c_168185,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(X1,X2),X2),X0))
      | c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_166716]) ).

tcf(c_168186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166716,c_560]) ).

tcf(c_168187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166716,c_564]) ).

tcf(c_168188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a)
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166716,c_562]) ).

tcf(c_168189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(t_a,t_a)),c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a))),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166716,c_561]) ).

tcf(c_168190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_166716,c_565]) ).

tcf(c_168191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),X0))
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_166716,c_144852]) ).

tcf(c_168192,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X2))
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_166716,c_125973]) ).

tcf(c_168193,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X0,tc_prod(X1,X1)),X2))
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_166716,c_125887]) ).

tcf(c_168194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X3,tc_prod(X2,X2)),c_Pair(X4,X0,X2,X2)))
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_166716,c_633]) ).

tcf(c_168195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),c_Pair(X3,X0,X2,X2)))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_166716,c_776]) ).

tcf(c_168196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,X0,X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),c_Pair(X3,X4,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_166716,c_762]) ).

tcf(c_168197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X2)),c_Pair(X3,X4,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_166716,c_761]) ).

tcf(c_168198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X4,tc_prod(X2,X3)),c_Pair(X0,X5,X2,X3)))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_166716,c_642]) ).

tcf(c_168199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X4,tc_prod(X2,X5)),c_Pair(X0,X3,X2,X5)))
      | c_in(X3,c_Relation_OImage(c_Relation_ODomain(c_Relation_Oconverse(X4,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_166716,c_774]) ).

tcf(c_168200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),c_Pair(X4,X0,X2,X3)))
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_166716,c_770]) ).

tcf(c_168201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X1,tc_prod(X2,X3)),c_Pair(X0,X4,X2,X3)))
      | c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_166716,c_768]) ).

tcf(c_168202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X3))
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_166716,c_763]) ).

tcf(c_168203,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2))
      | hBOOL(hAPP(c_Relation_ODomain(c_Relation_Oconverse(X0,X1,X1),X1,X1),X2)) ),
    inference(superposition,[status(thm)],[c_166716,c_840]) ).

tcf(c_168204,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(X1,iPr_def_13),c_Pair(X0,X2,iPr_def_11,iPr_def_12)))
      | c_in(X0,c_Relation_ODomain(c_Relation_ODomain(c_Relation_Oconverse(X1,iPr_def_13,iPr_def_13),iPr_def_13,iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_166716,c_126501]) ).

tcf(c_168281,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_596,c_166721]) ).

tcf(c_168282,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(X1,X2),X3)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_670,c_166721]) ).

tcf(c_168283,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3)
      | c_in(X0,c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2),X2) ),
    inference(superposition,[status(thm)],[c_684,c_166721]) ).

tcf(c_168284,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_687,c_166721]) ).

tcf(c_168289,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2)),t_a,t_a),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166721,c_560]) ).

tcf(c_168290,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2)),t_a,t_a),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166721,c_564]) ).

tcf(c_168291,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2)),t_a,t_a),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166721,c_562]) ).

tcf(c_168292,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2)),t_a,t_a),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166721,c_561]) ).

tcf(c_168293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3),X3,X3),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_166721,c_565]) ).

tcf(c_168294,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,X2,X2),X2)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3),X4) ),
    inference(superposition,[status(thm)],[c_166721,c_144852]) ).

tcf(c_168295,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Relation_ODomain(X0,X1,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_166721,c_125973]) ).

tcf(c_168296,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Relation_ODomain(X0,X1,X1),X1)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2),X3)) ),
    inference(superposition,[status(thm)],[c_166721,c_125887]) ).

tcf(c_168297,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),c_Relation_ODomain(X3,X4,X4),X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_166721,c_633]) ).

tcf(c_168298,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3),X3)
      | c_in(c_Pair(X4,X0,X3,X3),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_166721,c_776]) ).

tcf(c_168299,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_166721,c_762]) ).

tcf(c_168300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),c_Relation_ODomain(X1,X2,X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_166721,c_761]) ).

tcf(c_168301,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X3),c_Relation_ODomain(X4,X5,X5),X5)
      | ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,X5,X5),X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,X5,X5),X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_166721,c_642]) ).

tcf(c_168302,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X6),c_Relation_ODomain(X4,X5,X5),X5)
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,X5,X5),X5),X1,X2,X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_166721,c_774]) ).

tcf(c_168303,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X3,X4),c_Relation_ODomain(X1,X2,X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3,X4),X4,X3),X4) ),
    inference(superposition,[status(thm)],[c_166721,c_770]) ).

tcf(c_168304,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X3,X4),c_Relation_ODomain(X1,X2,X2),X2)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3,X4),X3) ),
    inference(superposition,[status(thm)],[c_166721,c_768]) ).

tcf(c_168305,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Relation_ODomain(X0,X1,X1),X1)
      | c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_166721,c_763]) ).

tcf(c_168384,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2))
      | hBOOL(hAPP(c_Relation_ODomain(c_Relation_OId__on(X0,X1),X1,X1),X2)) ),
    inference(superposition,[status(thm)],[c_684,c_166781]) ).

tcf(c_168385,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(c_Transitive__Closure_Otrancl(X0,X1),X1,X1),X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_687,c_166781]) ).

tcf(c_168386,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X2,X3,X3),X3),X0))
      | hBOOL(hAPP(c_Relation_ODomain(X2,X3,X3),v_sko__Wellfounded__Xacc__Xinduct__1(c_Wellfounded_Oacc(c_Relation_Oconverse(X2,X3,X3),X3),X1)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166781,c_517]) ).

tcf(c_168387,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),X0))
      | hBOOL(hAPP(c_Relation_ODomain(X3,X4,X4),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),X1,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_166781,c_537]) ).

tcf(c_168388,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X1,X2,X2),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_166781,c_841]) ).

tcf(c_168392,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( hBOOL(hAPP(c_Relation_ODomain(X0,X1,X1),X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X0,X1,X1),X1),X1),X2)) ),
    inference(light_normalisation,[status(thm)],[c_168385,c_743]) ).

tcf(c_168405,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X1,X3)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_724,c_166921]) ).

tcf(c_168406,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,X2,X2),X3)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_743,c_166921]) ).

tcf(c_168410,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X3)
      | c_in(X0,c_Wellfounded_Oacc(c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_687,c_166921]) ).

tcf(c_168411,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Relation_ODomain(X1,X2,X2)),t_a,t_a),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_560]) ).

tcf(c_168412,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,c_Relation_ODomain(X1,X2,X2)),t_a,t_a),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_564]) ).

tcf(c_168413,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),t_a),t_a)
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Relation_ODomain(X1,X2,X2)),t_a,t_a),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_562]) ).

tcf(c_168414,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,c_Relation_ODomain(X1,X2,X2)),t_a,t_a),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_561]) ).

tcf(c_168415,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,c_Relation_ODomain(X1,X2,X2),X3),X3,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_565]) ).

tcf(c_168416,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X1,X2,X2),X3),X4)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_144852]) ).

tcf(c_168417,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Relation_ODomain(X1,X2,X2),X3),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_125973]) ).

tcf(c_168418,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Relation_ODomain(X1,X2,X2),X3),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_125887]) ).

tcf(c_168419,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X3,X4,X4),X4),X4)
      | c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Relation_ODomain(X3,X4,X4),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_ODomain(X3,X4,X4),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_166921,c_633]) ).

tcf(c_168420,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),X3),X3)
      | c_in(c_Pair(X4,X0,X3,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Relation_ODomain(X1,X2,X2),X3),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_776]) ).

tcf(c_168421,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(X1,X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_762]) ).

tcf(c_168422,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X3)
      | c_in(c_Pair(X4,X5,X3,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_ODomain(X1,X2,X2),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_761]) ).

tcf(c_168423,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X6,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,X5,X5),X5),X5)
      | ( X1 = X6 )
      | ~ c_Relation_Osingle__valued(c_Relation_ODomain(X4,X5,X5),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Relation_ODomain(X4,X5,X5),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_166921,c_642]) ).

tcf(c_168424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(c_Relation_ODomain(X5,X6,X6),X1,X2,X4),X4)
      | c_in(c_Pair(X0,X3,X2,X4),c_Wellfounded_Oacc(c_Relation_Oconverse(X5,X6,X6),X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_166921,c_774]) ).

tcf(c_168425,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(c_Relation_ODomain(X4,X5,X5),X2,X3),X3,X2),X3)
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,X5,X5),X5),X5) ),
    inference(superposition,[status(thm)],[c_166921,c_770]) ).

tcf(c_168426,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(c_Relation_ODomain(X4,X5,X5),X2,X3),X2)
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,X5,X5),X5),X5) ),
    inference(superposition,[status(thm)],[c_166921,c_768]) ).

tcf(c_168427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
      | ~ c_Relation_Orefl__on(c_Relation_ODomain(X0,X1,X1),X2,X3) ),
    inference(superposition,[status(thm)],[c_166921,c_763]) ).

tcf(c_168430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(c_Relation_Oconverse(X0,X1,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_511]) ).

tcf(c_168431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(X2,c_Relation_ODomain(X1,t_a,t_a),X3)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_Oconverse(X1,t_a,t_a)))) ),
    inference(superposition,[status(thm)],[c_166921,c_553]) ).

tcf(c_168432,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X1)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(c_Relation_Oconverse(X0,X1,X1),X2,X1),c_Relation_ODomain(X0,X1,X1),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_545]) ).

tcf(c_168433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,c_Relation_ODomain(X1,X2,X2),X4)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_Oconverse(X1,X2,X2),X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X1,X2,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_550]) ).

tcf(c_168434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_560]) ).

tcf(c_168435,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_564]) ).

tcf(c_168436,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_562]) ).

tcf(c_168437,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),c_Relation_ODomain(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(t_a,t_a),tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_166921,c_561]) ).

tcf(c_168438,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_565]) ).

tcf(c_168439,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),X4)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_144852]) ).

tcf(c_168440,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X3)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_166921,c_125973]) ).

tcf(c_168441,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,tc_prod(X1,X1),tc_prod(X1,X1)),X3)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,tc_prod(X1,X1),tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_166921,c_125887]) ).

tcf(c_168442,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X0,X2,X2),c_Relation_ODomain(X3,tc_prod(X2,X2),tc_prod(X2,X2)),X5)
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_Oconverse(X3,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_166921,c_633]) ).

tcf(c_168443,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X0,X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),X4)
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_776]) ).

tcf(c_168444,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),X5)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_762]) ).

tcf(c_168445,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Relation_ODomain(X1,tc_prod(X2,X2),tc_prod(X2,X2)),X5)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X2),tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_761]) ).

tcf(c_168446,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X3),c_Relation_ODomain(X4,tc_prod(X2,X3),tc_prod(X2,X3)),X6)
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_166921,c_642]) ).

tcf(c_168447,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X5),c_Relation_ODomain(X4,tc_prod(X2,X5),tc_prod(X2,X5)),X6)
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_Oconverse(X4,tc_prod(X2,X5),tc_prod(X2,X5)),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_166921,c_774]) ).

tcf(c_168448,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X0,X2,X3),c_Relation_ODomain(X1,tc_prod(X2,X3),tc_prod(X2,X3)),X5)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_166921,c_770]) ).

tcf(c_168449,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X3),c_Relation_ODomain(X1,tc_prod(X2,X3),tc_prod(X2,X3)),X5)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,tc_prod(X2,X3),tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_166921,c_768]) ).

tcf(c_168450,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Relation_ODomain(X0,X1,X1),X4)
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_166921,c_763]) ).

tcf(c_168451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,X1,X1),X3)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_Oconverse(X0,X1,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_166921,c_840]) ).

tcf(c_168452,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X2,iPr_def_11,iPr_def_12),c_Relation_ODomain(X1,iPr_def_13,iPr_def_13),X3)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_Oconverse(X1,iPr_def_13,iPr_def_13),iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_166921,c_126501]) ).

tcf(c_169174,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X0,X1,X3)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(demodulation,[status(thm)],[c_168405,c_684]) ).

tcf(c_169181,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X1,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X0,X2),X3),X3),X3) ),
    inference(superposition,[status(thm)],[c_169174,c_511]) ).

tcf(c_169182,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(X2,c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X1,t_a),X3),X3),X3)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1))) ),
    inference(superposition,[status(thm)],[c_169174,c_553]) ).

tcf(c_169183,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X1,c_Wellfounded_Oacc(X0,X2),X2)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X1,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X0,X2),X3),X3),X3) ),
    inference(superposition,[status(thm)],[c_169174,c_545]) ).

tcf(c_169184,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X1,X2),X3),X3),X3) ),
    inference(superposition,[status(thm)],[c_169174,c_550]) ).

tcf(c_169185,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X1),t_a,t_a),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X4),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_560]) ).

tcf(c_169186,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X1),t_a,t_a),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X4),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_564]) ).

tcf(c_169187,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(X1,t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X1),t_a,t_a),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X4),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_562]) ).

tcf(c_169188,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X1),t_a,t_a),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X4),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_561]) ).

tcf(c_169189,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X1,X2),X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X5),X5),X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_565]) ).

tcf(c_169190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X3),X4)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_144852]) ).

tcf(c_169191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,X3),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_125973]) ).

tcf(c_169192,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X1,X3),X0))
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_125887]) ).

tcf(c_169193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X4,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_793]) ).

tcf(c_169194,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,X4,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X5),X5),X5)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,X2,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,X2,X3),X3,X3),X2,tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169174,c_632]) ).

tcf(c_169195,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X4,X1,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X5),X5),X5)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X3,X3),X2,tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169174,c_631]) ).

tcf(c_169196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_847]) ).

tcf(c_169197,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X4,X1,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X5),X5),X5)
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169174,c_799]) ).

tcf(c_169198,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_798]) ).

tcf(c_169199,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,X4,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X5),X5),X5)
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169174,c_795]) ).

tcf(c_169200,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_849]) ).

tcf(c_169201,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_848]) ).

tcf(c_169202,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_782]) ).

tcf(c_169203,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_781]) ).

tcf(c_169204,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X1,X4,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X5),X5),X5)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,X2,X3))) ),
    inference(superposition,[status(thm)],[c_169174,c_794]) ).

tcf(c_169205,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X4))
      | c_in(c_Pair(X4,X1,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X5),X5),X5)
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3))) ),
    inference(superposition,[status(thm)],[c_169174,c_784]) ).

tcf(c_169206,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X4,X3)))
      | c_in(c_Pair(X2,X1,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X4,X3),X5),X5),X5)
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169174,c_800]) ).

tcf(c_169207,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X2))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,X4,X3)))
      | c_in(c_Pair(X1,X2,X3,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X4,X3),X5),X5),X5)
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169174,c_786]) ).

tcf(c_169208,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169174,c_789]) ).

tcf(c_169209,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(c_Pair(X3,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X1,X2),X4),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_809]) ).

tcf(c_169210,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(X3,X2,X2),X2)
      | c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169174,c_806]) ).

tcf(c_169211,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_633]) ).

tcf(c_169212,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
      | c_in(c_Pair(X3,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X4),X4),X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_776]) ).

tcf(c_169213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X5),X5),X5)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169174,c_762]) ).

tcf(c_169214,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X5),X5),X5)
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169174,c_761]) ).

tcf(c_169215,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_797]) ).

tcf(c_169216,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_634]) ).

tcf(c_169217,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X4,X0,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_638]) ).

tcf(c_169218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X4,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X5),X5),X5)
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_637]) ).

tcf(c_169219,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X4),X4),X4) ),
    inference(superposition,[status(thm)],[c_169174,c_796]) ).

tcf(c_169220,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X3,X2)
      | c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(X3,X2),X4),X4),X4) ),
    inference(superposition,[status(thm)],[c_169174,c_772]) ).

tcf(c_169221,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(X3,X2),X4),X4),X4)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169174,c_635]) ).

tcf(c_169222,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2))
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_Oconverse(X4,X3,X2),X5),X5),X5) ),
    inference(superposition,[status(thm)],[c_169174,c_639]) ).

tcf(c_169223,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,X6),X6),X6)
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(X4,X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_169174,c_642]) ).

tcf(c_169224,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X3,c_Relation_OImage(X5,X1,X2,X4),X4)
      | c_in(c_Pair(X0,X3,X2,X4),c_Wellfounded_Oacc(c_Relation_OId__on(X5,X6),X6),X6)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169174,c_774]) ).

tcf(c_169225,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X1,c_Relation_ODomain(c_Relation_Oconverse(X4,X2,X3),X3,X2),X3)
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X5) ),
    inference(superposition,[status(thm)],[c_169174,c_770]) ).

tcf(c_169226,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,X5),X5),X5) ),
    inference(superposition,[status(thm)],[c_169174,c_768]) ).

tcf(c_169227,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X0,X4),X4),X4)
      | c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169174,c_763]) ).

tcf(c_169229,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X1,hAPP(X5,X0),X3)
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Product__Type_OSigma(X4,X5,X2,X3),X6),X6),X6) ),
    inference(superposition,[status(thm)],[c_169174,c_766]) ).

tcf(c_169230,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X0,X4,X2)
      | c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(c_Product__Type_OSigma(X4,X5,X2,X3),X6),X6),X6) ),
    inference(superposition,[status(thm)],[c_169174,c_765]) ).

tcf(c_169231,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X1,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X3,X2,X2),X2),X4),X4),X4) ),
    inference(superposition,[status(thm)],[c_169174,c_791]) ).

tcf(c_169232,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X1,X5,X3,X3),X7,tc_prod(X3,X3))
      | c_in(c_Pair(X0,X4,X2,X2),X6,tc_prod(X2,X2))
      | c_in(c_Pair(c_Pair(X0,X1,X2,X3),c_Pair(X4,X5,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)),c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Olex__prod(X6,X7,X2,X3),X8),X8),X8) ),
    inference(superposition,[status(thm)],[c_169174,c_811]) ).

tcf(c_169233,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),X6,tc_prod(X3,X3))
      | c_in(c_Pair(c_Pair(X0,X2,X3,X4),c_Pair(X1,X5,X3,X4),tc_prod(X3,X4),tc_prod(X3,X4)),c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Olex__prod(X6,X7,X3,X4),X8),X8),X8)
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169174,c_814]) ).

tcf(c_169234,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),X4)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X1,X2),X3),X3),X3) ),
    inference(superposition,[status(thm)],[c_169174,c_136744]) ).

tcf(c_169236,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X0,X2,X6)
      | c_in(c_Pair(c_Pair(X3,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Wellfounded_Oacc(c_Relation_OId__on(c_SmallStep_Ored(X0),X7),X7),X7)
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X2,X1)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,X4) ),
    inference(superposition,[status(thm)],[c_169174,c_149320]) ).

tcf(c_169237,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_Objects_Ohext(X1,X4)
      | c_in(c_Pair(c_Pair(X0,c_Pair(X1,X2,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X3,c_Pair(X4,X5,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Wellfounded_Oacc(c_Relation_OId__on(c_SmallStep_Ored(X6),X7),X7),X7) ),
    inference(superposition,[status(thm)],[c_169174,c_149692]) ).

tcf(c_169238,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( c_in(c_Pair(c_Pair(X5,X8,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X9,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X10),X10),X10)
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X5,X6,X7,X0,iPr_def_10),X8,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_169174,c_160855]) ).

tcf(c_169239,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( c_in(c_Pair(c_Pair(X5,X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X9),X9),X9)
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X5,X6,X0,iPr_def_10),X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_169174,c_160402]) ).

tcf(c_169240,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(c_Pair(X5,X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X7,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8),X8),X8)
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X5,X0,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_169174,c_160389]) ).

tcf(c_169242,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X2))
      | c_in(X2,X1,X3)
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,c_Relation_OId__on(X1,t_a)))) ),
    inference(superposition,[status(thm)],[c_169174,c_553]) ).

tcf(c_169244,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X0,X3))
      | c_in(X3,X1,X4)
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,c_Relation_OId__on(X1,X2),X2),c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_550]) ).

tcf(c_169245,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_560]) ).

tcf(c_169246,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinduct__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_564]) ).

tcf(c_169247,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X0))
      | c_in(X2,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a)
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_562]) ).

tcf(c_169248,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X3,X2))
      | hBOOL(hAPP(X3,X0))
      | c_in(c_Pair(X2,v_sko__Wellfounded__Xacc__Xinducts__1(X3,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a))),t_a,t_a),X1,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(t_a,t_a)),tc_prod(t_a,t_a)),t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169174,c_561]) ).

tcf(c_169249,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2,X2),X1,X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_565]) ).

tcf(c_169250,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X1,X4)
      | c_in(X0,c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X3) ),
    inference(superposition,[status(thm)],[c_169174,c_144852]) ).

tcf(c_169251,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,X0,X3)
      | hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_125973]) ).

tcf(c_169252,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,X0,X3)
      | hBOOL(hAPP(c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X0,tc_prod(X1,X1)),tc_prod(X1,X1)),X1),X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_125887]) ).

tcf(c_169253,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X0,X2,X2),X3,X5)
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(c_Wellfounded_Oacc(c_Relation_OId__on(X3,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Wellfounded_Oacc(c_Relation_OId__on(X3,tc_prod(X2,X2)),tc_prod(X2,X2)),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_633]) ).

tcf(c_169254,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X0,X2,X2),X1,X4)
      | c_in(X3,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2)
      | ~ c_in(X0,c_Wellfounded_Oacc(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_776]) ).

tcf(c_169255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),X1,X5)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_762]) ).

tcf(c_169256,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,X0,X2)
      | c_in(c_Pair(X3,X4,X2,X2),X1,X5)
      | ~ c_Relation_Orefl__on(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X2)),tc_prod(X2,X2)),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_761]) ).

tcf(c_169257,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X5,X2,X3),X4,X6)
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X3)),tc_prod(X2,X3)),tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_169174,c_642]) ).

tcf(c_169258,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(c_Pair(X0,X3,X2,X5),X4,X6)
      | c_in(X3,c_Relation_OImage(c_Wellfounded_Oacc(c_Relation_OId__on(X4,tc_prod(X2,X5)),tc_prod(X2,X5)),X1,X2,X5),X5)
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169174,c_774]) ).

tcf(c_169259,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X4,X0,X2,X3),X1,X5)
      | c_in(X0,c_Relation_ODomain(c_Relation_Oconverse(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X3,X2),X3) ),
    inference(superposition,[status(thm)],[c_169174,c_770]) ).

tcf(c_169260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X4,X2,X3),X1,X5)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,tc_prod(X2,X3)),tc_prod(X2,X3)),X2,X3),X2) ),
    inference(superposition,[status(thm)],[c_169174,c_768]) ).

tcf(c_169261,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X4)
      | c_in(c_Pair(X3,X3,X1,X1),X2,tc_prod(X1,X1))
      | ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2,X1) ),
    inference(superposition,[status(thm)],[c_169174,c_763]) ).

tcf(c_169262,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X2,X0,X3)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_169174,c_840]) ).

tcf(c_169263,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(c_Pair(X0,X2,iPr_def_11,iPr_def_12),X1,X3)
      | c_in(X0,c_Relation_ODomain(c_Wellfounded_Oacc(c_Relation_OId__on(X1,iPr_def_13),iPr_def_13),iPr_def_11,iPr_def_12),iPr_def_11) ),
    inference(superposition,[status(thm)],[c_169174,c_126501]) ).

tcf(c_169631,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X0,X1),X2),X2),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X0,X3,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_511]) ).

tcf(c_169632,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(X0,X3))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X1,t_a),X2),X2),X3))
      | ~ hBOOL(hAPP(X0,v_sko__Wellfounded__Xacc__Xinducts__1(X0,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_553]) ).

tcf(c_169633,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( c_in(X3,c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X0,X1),X2),X2),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X0,X3,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_545]) ).

tcf(c_169634,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X0,X1),c_Wellfounded_Oacc(X0,X1),X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Oacc(X0,X1),X2),X2),X3)) ),
    inference(superposition,[status(thm)],[c_169262,c_550]) ).

tcf(c_169635,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(X1,t_a),t_a)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X1),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169262,c_560]) ).

tcf(c_169636,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X1),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169262,c_564]) ).

tcf(c_169637,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X0))
      | c_in(X3,c_Wellfounded_Oacc(X1,t_a),t_a)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X1),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169262,c_562]) ).

tcf(c_169638,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(X4,X3))
      | hBOOL(hAPP(X4,X0))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X1),t_a,t_a)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169262,c_561]) ).

tcf(c_169639,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X5,X4))
      | hBOOL(hAPP(X5,X0))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X3),X3),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X1,X2),X2,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169262,c_565]) ).

tcf(c_169640,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X2,c_Transitive__Closure_Ortrancl(X0,X3),X4)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_144852]) ).

tcf(c_169641,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X0,X3),X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_125973]) ).

tcf(c_169642,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( hBOOL(hAPP(c_Transitive__Closure_Otrancl(X0,X3),X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_125887]) ).

tcf(c_169643,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | c_in(c_Pair(X1,X5,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X0,X5,X2,X2)))
      | ~ c_Relation_Osingle__valued(X3,X2,X2)
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_793]) ).

tcf(c_169644,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X1,X5,X3,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,X2,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,X2,X3),X3,X3),X2,tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169262,c_632]) ).

tcf(c_169645,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X5,X1,X3,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X3,X3),X2,tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169262,c_631]) ).

tcf(c_169646,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_847]) ).

tcf(c_169647,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X5,X1,X3,X3)))
      | c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3),X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169262,c_799]) ).

tcf(c_169648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_798]) ).

tcf(c_169649,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X1,X5,X3,X3)))
      | c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169262,c_795]) ).

tcf(c_169650,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_849]) ).

tcf(c_169651,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X1,X5,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_848]) ).

tcf(c_169652,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_782]) ).

tcf(c_169653,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X3,X2),X4),X4),c_Pair(X1,X5,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_781]) ).

tcf(c_169654,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X1,X5,X3,X3)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X0,X1,X2,X3))) ),
    inference(superposition,[status(thm)],[c_169262,c_794]) ).

tcf(c_169655,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X5,X1,X3,X3)))
      | ~ hBOOL(hAPP(X0,X1))
      | ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X0,X1,X2,X3))) ),
    inference(superposition,[status(thm)],[c_169262,c_784]) ).

tcf(c_169656,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X0,X1,X2,X3)))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X5,X1,X3,X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169262,c_800]) ).

tcf(c_169657,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X0,X1,X2,X3)))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X1,X5,X3,X3)))
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(superposition,[status(thm)],[c_169262,c_786]) ).

tcf(c_169658,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X0,X1,X3,X3),c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X0,X1,X3,X3)))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169262,c_789]) ).

tcf(c_169659,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(X1,X2),X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X1,X2),X3),X3),c_Pair(X4,X0,X2,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169262,c_809]) ).

tcf(c_169660,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,c_Relation_ODomain(X2,X3,X3),X3)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X2,X3),X4),X4),c_Pair(X0,X1,X3,X3)))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169262,c_806]) ).

tcf(c_169661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X5),X5),c_Pair(X4,X0,X2,X2)))
      | c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_633]) ).

tcf(c_169662,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X4,c_Wellfounded_Oacc(X1,X2),X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X3),X3),c_Pair(X4,X0,X2,X2)))
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169262,c_776]) ).

tcf(c_169663,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X5,X0,X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X3),X3),c_Pair(X4,X5,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169262,c_762]) ).

tcf(c_169664,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X4,X0,X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X1,X3),X3),c_Pair(X4,X5,X2,X2)))
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169262,c_761]) ).

tcf(c_169665,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_797]) ).

tcf(c_169666,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_634]) ).

tcf(c_169667,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X4),X4),c_Pair(X5,X0,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_638]) ).

tcf(c_169668,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X0,X5,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X3,X2),X4),X4),c_Pair(X1,X5,X2,X2)))
      | ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
    inference(superposition,[status(thm)],[c_169262,c_637]) ).

tcf(c_169669,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X3,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Otrancl(X0,X1),X2),X2),c_Pair(X3,X4,X1,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_796]) ).

tcf(c_169670,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,X0,X1)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(X0,X1),X2),X2),c_Pair(X3,X4,X1,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_772]) ).

tcf(c_169671,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_OId__on(X2,X3),X4),X4),c_Pair(X0,X1,X3,X3)))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169262,c_635]) ).

tcf(c_169672,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(c_Pair(X5,X4,X1,X2),X0,tc_prod(X1,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Relation_Oconverse(X0,X1,X2),X3),X3),c_Pair(X4,X5,X2,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_639]) ).

tcf(c_169673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X4,X6),X6),c_Pair(X0,X5,X2,X3)))
      | ( X1 = X5 )
      | ~ c_Relation_Osingle__valued(X4,X2,X3)
      | ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
    inference(superposition,[status(thm)],[c_169262,c_642]) ).

tcf(c_169674,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,c_Relation_OImage(X3,X1,X2,X6),X6)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),c_Pair(X0,X5,X2,X6)))
      | ~ c_in(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169262,c_774]) ).

tcf(c_169675,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X3,c_Relation_ODomain(c_Relation_Oconverse(X0,X4,X5),X5,X4),X5)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),c_Pair(X2,X3,X4,X5))) ),
    inference(superposition,[status(thm)],[c_169262,c_770]) ).

tcf(c_169676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( c_in(X2,c_Relation_ODomain(X0,X4,X5),X4)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X1),X1),c_Pair(X2,X3,X4,X5))) ),
    inference(superposition,[status(thm)],[c_169262,c_768]) ).

tcf(c_169677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X0,X4),X4),X3))
      | c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
      | ~ c_Relation_Orefl__on(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_169262,c_763]) ).

tcf(c_169679,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X6,hAPP(X1,X5),X3)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Product__Type_OSigma(X0,X1,X2,X3),X4),X4),c_Pair(X5,X6,X2,X3))) ),
    inference(superposition,[status(thm)],[c_169262,c_766]) ).

tcf(c_169680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( c_in(X5,X0,X2)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Product__Type_OSigma(X0,X1,X2,X3),X4),X4),c_Pair(X5,X6,X2,X3))) ),
    inference(superposition,[status(thm)],[c_169262,c_765]) ).

tcf(c_169681,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(c_Pair(X4,X3,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X0,X1,X1),X1),X2),X2),c_Pair(X3,X4,X1,X1))) ),
    inference(superposition,[status(thm)],[c_169262,c_791]) ).

tcf(c_169682,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X6,X8,X3,X3),X1,tc_prod(X3,X3))
      | c_in(c_Pair(X5,X7,X2,X2),X0,tc_prod(X2,X2))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Olex__prod(X0,X1,X2,X3),X4),X4),c_Pair(c_Pair(X5,X6,X2,X3),c_Pair(X7,X8,X2,X3),tc_prod(X2,X3),tc_prod(X2,X3)))) ),
    inference(superposition,[status(thm)],[c_169262,c_811]) ).

tcf(c_169683,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( c_in(c_Pair(X0,X1,X4,X4),X2,tc_prod(X4,X4))
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Wellfounded_Olex__prod(X2,X3,X4,X5),X6),X6),c_Pair(c_Pair(X0,X7,X4,X5),c_Pair(X1,X8,X4,X5),tc_prod(X4,X5),tc_prod(X4,X5))))
      | ( X0 = X1 ) ),
    inference(superposition,[status(thm)],[c_169262,c_814]) ).

tcf(c_169684,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X3,c_Transitive__Closure_Ortrancl(X0,X1),X4)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(X0,X1),X2),X2),X3)) ),
    inference(superposition,[status(thm)],[c_169262,c_136744]) ).

tcf(c_169686,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_TypeSafe__Mirabelle_Osconf(X0,X2,X7)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_SmallStep_Ored(X0),X5),X5),c_Pair(c_Pair(X3,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X6,X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | ~ c_TypeSafe__Mirabelle_Osconf(X0,X2,X1)
      | ~ c_WellTypeRT_OWTrt(X0,c_State_Ohp(X1),X2,X3,X4) ),
    inference(superposition,[status(thm)],[c_169262,c_149320]) ).

tcf(c_169687,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( c_Objects_Ohext(X3,X6)
      | hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_SmallStep_Ored(X0),X1),X1),c_Pair(c_Pair(X2,c_Pair(X3,X4,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X5,c_Pair(X6,X7,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))),iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))) ),
    inference(superposition,[status(thm)],[c_169262,c_149692]) ).

tcf(c_169688,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X9),X9),c_Pair(c_Pair(X5,X8,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X10,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OFAss(X5,X6,X7,X0,iPr_def_10),X8,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_169262,c_160855]) ).

tcf(c_169689,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X8),X8),c_Pair(c_Pair(X5,X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X9,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OBinOp(X5,X6,X0,iPr_def_10),X7,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_Othrow(X2,iPr_def_10),X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_169262,c_160402]) ).

tcf(c_169690,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),X7),X7),c_Pair(c_Pair(X5,X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(c_Expr_Oexp_OVal(X8,iPr_def_10),X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))))
      | c_in(c_Pair(c_Pair(c_Expr_Oexp_OSeq(X5,X0,iPr_def_10),X6,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))))
      | ~ c_in(c_Pair(c_Pair(X0,X1,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),c_Pair(X2,X3,iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),c_Transitive__Closure_Ortrancl(c_SmallStep_Ored(X4),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval))))),tc_prod(tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))),tc_prod(iPr_def_12,tc_prod(tc_fun(tc_nat,tc_Option_Ooption(tc_prod(iPr_def_10,tc_fun(tc_prod(iPr_def_10,iPr_def_10),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(iPr_def_10,tc_Option_Ooption(tc_Value_Oval)))))) ),
    inference(superposition,[status(thm)],[c_169262,c_160389]) ).

tcf(c_169691,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X0))
      | c_in(v_sko__Wellfounded__Xacc__Xinduct__1(c_Wellfounded_Oacc(c_Relation_OId__on(X2,X3),X3),X1),X2,X4)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,t_a),t_a) ),
    inference(superposition,[status(thm)],[c_169262,c_517]) ).

tcf(c_169692,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( hBOOL(hAPP(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X0))
      | c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(c_Wellfounded_Oacc(c_Relation_OId__on(X3,X4),X4),X1,X2),X3,X5)
      | ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
    inference(superposition,[status(thm)],[c_169262,c_537]) ).

tcf(c_169693,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( c_in(X0,X1,X4)
      | c_in(X0,c_Wellfounded_Oacc(c_Relation_OId__on(X1,X2),X2),X3) ),
    inference(superposition,[status(thm)],[c_169262,c_841]) ).

tcf(c_170216,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_168384,c_168281,c_168182,c_168053,c_167975,c_166920,c_166756,c_166715,c_166387,c_166098,c_165895,c_165779,c_165411,c_164990,c_164970,c_164969,c_164933,c_164790,c_164729,c_164680,c_164661,c_164523,c_164480,c_164440,c_164393,c_164349,c_164063,c_164008,c_163947,c_163899,c_163861,c_163821,c_163589,c_163543,c_163426,c_163368,c_163309,c_163269,c_163147,c_163072,c_163021,c_162953,c_162821,c_162746,c_162715,c_162707,c_161800,c_161625,c_161543,c_161292,c_161033,c_160939,c_160889,c_160623,c_160549,c_160475,c_160449,c_160435,c_160375,c_160224,c_160211,c_160189,c_160124,c_160059,c_159994,c_159950,c_159727,c_159655,c_159105,c_159097,c_159096,c_159083,c_159082,c_159006,c_158998,c_158997,c_158954,c_158889,c_158824,c_158759,c_158585,c_158577,c_158576,c_158462,c_158454,c_158453,c_158377,c_158369,c_158368,c_158356,c_158225,c_158217,c_158216,c_151860,c_142736,c_142735,c_142479,c_142478,c_140298,c_140297,c_140296,c_140295,c_138458,c_138457,c_138156,c_138155,c_132511,c_131396,c_130979,c_130460,c_130165,c_129557,c_128494,c_128491,c_128169,c_128166,c_127790,c_127255,c_126903,c_126801,c_126730,c_126727,c_126725,c_126604,c_126603,c_126602,c_126601,c_126600,c_126599,c_126598,c_126597,c_126596,c_126595,c_126594,c_126593,c_126592,c_126451,c_126438,c_126437,c_126436,c_126435,c_126434,c_126433,c_126432,c_126431,c_126418,c_126414,c_126338,c_126261,c_126257,c_126186,c_126118,c_126113,c_126047,c_125957,c_125954,c_125953,c_125893,c_125890,c_125847,c_125827,c_125804,c_125724,c_125715,c_125701,c_125589,c_125588,c_125587,c_125586,c_125585,c_125584,c_125583,c_125582,c_125581,c_125580,c_125579,c_125578,c_125426,c_125420,c_125414,c_125378,c_125373,c_125371,c_125367,c_125365,c_125362,c_125356,c_125352,c_125349,c_125338,c_125336,c_125334,c_125320,c_139958,c_137813,c_135638,c_135637,c_134168,c_169693,c_169692,c_169691,c_169690,c_169689,c_169688,c_169687,c_169686,c_169684,c_169683,c_169682,c_169681,c_169680,c_169679,c_169677,c_169676,c_169675,c_169674,c_169673,c_169672,c_169671,c_169670,c_169669,c_169668,c_169667,c_169666,c_169665,c_169664,c_169663,c_169662,c_169661,c_169660,c_169659,c_169658,c_169657,c_169656,c_169655,c_169654,c_169653,c_169652,c_169651,c_169650,c_169649,c_169648,c_169647,c_169646,c_169645,c_169644,c_169643,c_169642,c_169641,c_169640,c_169639,c_169638,c_169637,c_169636,c_169635,c_169634,c_169633,c_169632,c_169631,c_169263,c_169262,c_169261,c_169260,c_169259,c_169258,c_169257,c_169256,c_169255,c_169254,c_169253,c_169252,c_169251,c_169250,c_169249,c_169248,c_169247,c_169246,c_169245,c_169244,c_169242,c_169240,c_169239,c_169238,c_169237,c_169236,c_169234,c_169233,c_169232,c_169231,c_169230,c_169229,c_169227,c_169226,c_169225,c_169224,c_169223,c_169222,c_169221,c_169220,c_169219,c_169218,c_169217,c_169216,c_169215,c_169214,c_169213,c_169212,c_169211,c_169210,c_169209,c_169208,c_169207,c_169206,c_169205,c_169204,c_169203,c_169202,c_169201,c_169200,c_169199,c_169198,c_169197,c_169196,c_169195,c_169194,c_169193,c_169192,c_169191,c_169190,c_169189,c_169188,c_169187,c_169186,c_169185,c_169184,c_169183,c_169182,c_169181,c_169174,c_168452,c_168451,c_168450,c_168449,c_168448,c_168447,c_168446,c_168445,c_168444,c_168443,c_168442,c_168441,c_168440,c_168439,c_168438,c_168437,c_168436,c_168435,c_168434,c_168433,c_168432,c_168431,c_168430,c_168427,c_168426,c_168425,c_168424,c_168423,c_168422,c_168421,c_168420,c_168419,c_168418,c_168417,c_168416,c_168415,c_168414,c_168413,c_168412,c_168411,c_168410,c_168406,c_168405,c_168392,c_168388,c_168387,c_168386,c_168385,c_168305,c_168304,c_168303,c_168302,c_168301,c_168300,c_168299,c_168298,c_168297,c_168296,c_168295,c_168294,c_168293,c_168292,c_168291,c_168290,c_168289,c_168284,c_168283,c_168282,c_168204,c_168203,c_168202,c_168201,c_168200,c_168199,c_168198,c_168197,c_168196,c_168195,c_168194,c_168193,c_168192,c_168191,c_168190,c_168189,c_168188,c_168187,c_168186,c_168185,c_168143,c_168140,c_168120,c_168119,c_168118,c_168117,c_168114,c_168113,c_168111,c_168110,c_168109,c_168108,c_168107,c_168106,c_168099,c_168097,c_168094,c_168074,c_168073,c_168072,c_168071,c_168068,c_168067,c_168065,c_168064,c_168063,c_168062,c_168061,c_168060,c_168019,c_168016,c_167996,c_167995,c_167994,c_167993,c_167990,c_167989,c_167987,c_167986,c_167985,c_167984,c_167983,c_167982,c_167770,c_167767,c_167747,c_167746,c_167745,c_167744,c_167741,c_167740,c_167738,c_167737,c_167736,c_167735,c_167734,c_167733,c_167727,c_167108,c_167107,c_167106,c_167105,c_167104,c_167103,c_167102,c_167101,c_167100,c_167099,c_167098,c_167097,c_167714,c_167713,c_167712,c_167696,c_167695,c_167480,c_167479,c_167478,c_167477,c_167476,c_167475,c_167474,c_167473,c_167472,c_167471,c_167469,c_167468,c_167467,c_167466,c_167465,c_167464,c_167462,c_167461,c_167460,c_167459,c_167458,c_167457,c_167456,c_167455,c_167454,c_167453,c_167452,c_167451,c_167450,c_167449,c_167448,c_167447,c_167446,c_167432,c_167431,c_167430,c_167417,c_167416,c_167177,c_167176,c_167175,c_167174,c_167173,c_167172,c_167171,c_167170,c_167169,c_167168,c_167166,c_167165,c_167164,c_167163,c_167162,c_167161,c_167159,c_167158,c_167157,c_167156,c_167155,c_167154,c_167153,c_167152,c_167151,c_167150,c_167149,c_167148,c_167147,c_167146,c_167145,c_167144,c_167143,c_166940,c_166939,c_166938,c_166937,c_166936,c_166935,c_166934,c_166933,c_166932,c_166931,c_166930,c_166929,c_166928,c_166927,c_166926,c_166925,c_166924,c_166923,c_166922,c_166921,c_166782,c_166781,c_166780,c_166779,c_166778,c_166777,c_166776,c_166775,c_166774,c_166773,c_166772,c_166771,c_166770,c_166769,c_166768,c_166767,c_166766,c_166765,c_166764,c_166763,c_166762,c_166761,c_166760,c_166759,c_166728,c_166721,c_166720,c_166719,c_166718,c_166717,c_166716,c_166695,c_166692,c_166672,c_166671,c_166670,c_166669,c_166666,c_166665,c_166663,c_166662,c_166661,c_166660,c_166659,c_166658,c_166620,c_166617,c_166597,c_166596,c_166595,c_166594,c_166591,c_166590,c_166588,c_166587,c_166586,c_166585,c_166584,c_166583,c_166561,c_166558,c_166538,c_166537,c_166536,c_166535,c_166532,c_166531,c_166529,c_166528,c_166527,c_166526,c_166525,c_166524,c_166502,c_166499,c_166479,c_166478,c_166477,c_166476,c_166473,c_166472,c_166470,c_166469,c_166468,c_166467,c_166466,c_166465,c_166430,c_166427,c_166407,c_166406,c_166405,c_166404,c_166401,c_166400,c_166398,c_166397,c_166396,c_166395,c_166394,c_166393,c_166386,c_166383,c_166363,c_166362,c_166361,c_166360,c_166357,c_166356,c_166354,c_166353,c_166352,c_166351,c_166350,c_166349,c_166142,c_166139,c_166119,c_166118,c_166117,c_166116,c_166113,c_166112,c_166110,c_166109,c_166108,c_166107,c_166106,c_166105,c_166058,c_166055,c_166035,c_166034,c_166033,c_166032,c_166029,c_166028,c_166026,c_166025,c_166024,c_166023,c_166022,c_166021,c_165937,c_165934,c_165914,c_165913,c_165912,c_165911,c_165908,c_165907,c_165905,c_165904,c_165903,c_165902,c_165901,c_165900,c_165865,c_165862,c_165842,c_165841,c_165840,c_165839,c_165836,c_165835,c_165833,c_165832,c_165831,c_165830,c_165829,c_165828,c_165822,c_165819,c_165799,c_165798,c_165797,c_165796,c_165793,c_165792,c_165790,c_165789,c_165788,c_165787,c_165786,c_165785,c_165778,c_165775,c_165755,c_165754,c_165753,c_165752,c_165749,c_165748,c_165746,c_165745,c_165744,c_165743,c_165742,c_165741,c_165985,c_165984,c_165983,c_165982,c_165981,c_165980,c_165951,c_165950,c_165949,c_165948,c_165947,c_165946,c_165635,c_165634,c_165633,c_165632,c_165631,c_165630,c_165629,c_165628,c_165627,c_165626,c_165625,c_165624,c_165423,c_165422,c_165421,c_165420,c_165419,c_165418,c_165417,c_165416,c_165415,c_165414,c_165413,c_165412,c_165324,c_165323,c_165322,c_165321,c_165320,c_165319,c_165315,c_165314,c_165313,c_165312,c_165311,c_165310,c_165309,c_165308,c_165307,c_165306,c_165305,c_165304,c_165303,c_165129,c_165128,c_165127,c_165126,c_165125,c_165124,c_165120,c_165119,c_165118,c_165117,c_165116,c_165115,c_165114,c_165113,c_165112,c_165111,c_165110,c_165109,c_165108,c_165018,c_165015,c_164995,c_164994,c_164993,c_164992,c_164984,c_164983,c_164981,c_164980,c_164979,c_164978,c_164977,c_164976,c_164961,c_164958,c_164938,c_164937,c_164936,c_164935,c_164927,c_164926,c_164924,c_164923,c_164922,c_164921,c_164920,c_164919,c_164914,c_164913,c_164818,c_164815,c_164795,c_164794,c_164793,c_164792,c_164784,c_164783,c_164781,c_164780,c_164779,c_164778,c_164777,c_164776,c_164757,c_164754,c_164734,c_164733,c_164732,c_164731,c_164723,c_164722,c_164720,c_164719,c_164718,c_164717,c_164716,c_164715,c_164708,c_164705,c_164685,c_164684,c_164683,c_164682,c_164674,c_164673,c_164671,c_164670,c_164669,c_164668,c_164667,c_164666,c_164551,c_164548,c_164528,c_164527,c_164526,c_164525,c_164517,c_164516,c_164514,c_164513,c_164512,c_164511,c_164510,c_164509,c_164485,c_164484,c_164483,c_164482,c_164481,c_164476,c_164475,c_164474,c_164473,c_164472,c_164471,c_164470,c_164469,c_164468,c_164465,c_164445,c_164444,c_164443,c_164442,c_164434,c_164433,c_164431,c_164430,c_164429,c_164428,c_164427,c_164426,c_164421,c_164418,c_164398,c_164397,c_164396,c_164395,c_164387,c_164386,c_164384,c_164383,c_164382,c_164381,c_164380,c_164379,c_164354,c_164353,c_164352,c_164351,c_164350,c_164345,c_164344,c_164343,c_164342,c_164341,c_164340,c_164339,c_164338,c_164068,c_164067,c_164066,c_164065,c_164064,c_164059,c_164058,c_164057,c_164056,c_164055,c_164054,c_164053,c_164052,c_164013,c_164012,c_164011,c_164010,c_164009,c_164004,c_164003,c_164002,c_164001,c_164000,c_163999,c_163998,c_163997,c_163952,c_163951,c_163950,c_163949,c_163948,c_163943,c_163942,c_163941,c_163940,c_163939,c_163938,c_163937,c_163936,c_163904,c_163903,c_163902,c_163901,c_163900,c_163895,c_163894,c_163893,c_163892,c_163891,c_163890,c_163889,c_163888,c_163866,c_163865,c_163864,c_163863,c_163862,c_163857,c_163856,c_163855,c_163854,c_163853,c_163852,c_163851,c_163850,c_163826,c_163825,c_163824,c_163823,c_163822,c_163817,c_163816,c_163815,c_163814,c_163813,c_163812,c_163811,c_163810,c_163594,c_163593,c_163592,c_163591,c_163590,c_163585,c_163584,c_163583,c_163582,c_163581,c_163580,c_163579,c_163578,c_163548,c_163547,c_163546,c_163545,c_163544,c_163539,c_163538,c_163537,c_163536,c_16353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).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV990-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36  % Computer : n008.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Thu Sep 24 21:29:39 UTC 2026
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39  Running first-order theorem proving
% 0.13/0.39  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40  
% 0.13/0.40  % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40  
% 0.13/0.40  % Detected problem language: tptp
% 0.13/0.42  % Proving...
% 138.77/20.96  % SZS status Started for theBenchmark.p
% 138.77/20.96  % SZS status Unsatisfiable for theBenchmark.p
% 138.77/20.96  
% 138.77/20.96  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 138.77/20.96  
% 138.77/20.96  % ------  iProver source info
% 138.77/20.96  
% 138.77/20.96  % git: date: 2026-07-19 20:42:38 +0200
% 138.77/20.96  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 138.77/20.96  % git: non_committed_changes: false
% 138.77/20.96  
% 138.77/20.96  % ------ Parsing...% successful
% 138.77/20.96  
% 138.77/20.96  
% 138.77/20.96  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 138.77/20.96  
% 138.77/20.96  % ------ Preprocessing... sup_sim: 5  sf_s  rm: 10 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e % 
% 138.77/20.96  
% 138.77/20.96  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 138.77/20.96  
% 138.77/20.96  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 138.77/20.96  % ------ Proving...
% 138.77/20.96  % ------ Problem Properties 
% 138.77/20.96  
% 138.77/20.96  % 
% 138.77/20.96  % clauses                               304
% 138.77/20.96  % conjectures                           2
% 138.77/20.96  % EPR                                   6
% 138.77/20.96  % Horn                                  279
% 138.77/20.96  % unary                                 126
% 138.77/20.96  % binary                                107
% 138.77/20.96  % lits                                  577
% 138.77/20.96  % lits eq                               182
% 138.77/20.96  % fd_pure                               0
% 138.77/20.96  % fd_pseudo                             0
% 138.77/20.96  % fd_cond                               0
% 138.77/20.96  % fd_pseudo_cond                        49
% 138.77/20.96  % AC symbols                            0
% 138.77/20.96  
% 138.77/20.96  % ------ Schedule dynamic 5 is on 
% 138.77/20.96  
% 138.77/20.96  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 138.77/20.96  
% 138.77/20.96  
% 138.77/20.96  % ------ 
% 138.77/20.96  % Current options:
% 138.77/20.96  % ------ 
% 138.77/20.96  
% 138.77/20.96  
% 138.77/20.96  % 
% 138.77/20.96  
% 138.77/20.96  % ------ Proving...
% 138.77/20.96  % Proof_search_loop: time out after: 3924 full_loop iterations
% 138.77/20.96  
% 138.77/20.96  % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 138.77/20.96  
% 138.77/20.96  
% 138.77/20.96  % ------ 
% 138.77/20.96  % Current options:
% 138.77/20.96  % ------ 
% 138.77/20.96  
% 138.77/20.96  
% 138.77/20.96  % 
% 138.77/20.96  
% 138.77/20.96  % ------ Proving...
% 138.77/20.96  % 
% 138.77/20.96  
% 138.77/20.96  % SZS status Unsatisfiable for theBenchmark.p
% 138.77/20.96  
% 138.77/20.96  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 147.01/21.22  
% 147.01/21.22  
%------------------------------------------------------------------------------