%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT041-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 02:06:50 PM UTC 2026
% Result : Unsatisfiable 177.82s 23.14s
% Output : CNFRefutation 161.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 121
% Syntax : Number of formulae : 422 ( 22 unt; 96 def)
% Number of atoms : 2489 ( 380 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 3482 (1415 ~;1971 |; 0 &)
% ( 96 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 105 ( 103 usr; 97 prp; 0-4 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-6 aty)
% Number of variables : 778 ( 778 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V_a,V_A,T_a] : c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T_a,V_f,V_A,T_b] :
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [V_c,T_a,T_b,V_A] :
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f577,axiom,
! [V_a,V_b,T_a,T_b,V_r] :
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f589,axiom,
! [V_x,V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f591,axiom,
! [V_a,V_b,T_a,V_r] :
( ~ c_Relation_Oantisym(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_a = V_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f592,axiom,
! [V_f,V_y,V_z,T_a,V_r,T_b] :
( ~ c_Equiv__Relations_Ocongruent(V_r,V_f,T_a,T_b)
| ~ c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))
| hAPP(V_f,V_y) = hAPP(V_f,V_z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f601,axiom,
! [V_b,V_a,T_a,V_r] :
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_b,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f622,axiom,
! [V_a,V_r,T_a,V_b] :
( ~ c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f629,axiom,
! [V_x,V_A,T_a,V_y,V_r] :
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_x,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f630,axiom,
! [V_a,V_r,T_b,T_a,V_x] :
( ~ c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f632,axiom,
! [V_a,V_r,T_a,T_b,V_x] :
( ~ c_in(c_Pair(V_a,V_x,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f636,axiom,
! [V_xa,V_x,T_a,V_r,V_A] :
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_xa,V_A,T_a)
| V_x = V_xa
| c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f645,axiom,
! [V_a_H,V_b_H,V_P_H,V_a,V_b,V_P] :
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ c_in(V_P,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f646,axiom,
! [V_a_H,V_b_H,V_P_H,V_a,V_b,V_P] :
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ c_in(V_P,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f647,axiom,
! [V_i] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f648,axiom,
! [V_i] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f649,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f650,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f651,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f652,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f653,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f654,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f655,negated_conjecture,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f656,negated_conjecture,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f678,plain,
! [X0,X1,X2] : c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f689,plain,
! [V_A,T_b] :
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ! [T_a,V_f] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f690,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X1,X2,X3,X0) ),
inference(cnf_transformation,[status(thm)],[f689]) ).
fof(f858,plain,
! [T_b,V_A] :
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ! [V_c,T_a] : c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f859,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X3
| c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
inference(cnf_transformation,[status(thm)],[f858]) ).
fof(f1508,plain,
! [X0,X1,X2,X3,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)) ),
inference(cnf_transformation,[status(thm)],[f577]) ).
fof(f1526,plain,
! [T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ! [V_x,V_a] :
( ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(miniscoping,[status(thm)],[f589]) ).
fof(f1527,plain,
! [X0,X1,X2,X3] :
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f1526]) ).
fof(f1530,plain,
! [T_a,V_r] :
( ~ c_Relation_Oantisym(V_r,T_a)
| ! [V_a,V_b] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_a = V_b ) ),
inference(miniscoping,[status(thm)],[f591]) ).
fof(f1531,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Pair(X0,X1,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X0,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Oantisym(X2,X3)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1530]) ).
fof(f1532,plain,
! [V_f,T_a,V_r] :
( ! [T_b] : ~ c_Equiv__Relations_Ocongruent(V_r,V_f,T_a,T_b)
| ! [V_y,V_z] :
( ~ c_in(c_Pair(V_y,V_z,T_a,T_a),V_r,tc_prod(T_a,T_a))
| hAPP(V_f,V_y) = hAPP(V_f,V_z) ) ),
inference(miniscoping,[status(thm)],[f592]) ).
fof(f1533,plain,
! [X0,X1,X2,X3,X4,X5] :
( hAPP(X4,X0) = hAPP(X4,X1)
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X2,X5)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f1532]) ).
fof(f1550,plain,
! [T_a,V_r] :
( ~ c_Relation_Osym(V_r,T_a)
| ! [V_b,V_a] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_b,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(miniscoping,[status(thm)],[f601]) ).
fof(f1551,plain,
! [X0,X1,X2,X3] :
( c_in(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Relation_Osym(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1550]) ).
fof(f1583,plain,
! [V_r,T_a,V_b] :
( ~ c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ! [V_a] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a) ) ),
inference(miniscoping,[status(thm)],[f622]) ).
fof(f1584,plain,
! [X0,X1,X2,X3] :
( 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,[status(thm)],[f1583]) ).
fof(f1596,plain,
! [V_A,T_a,V_r] :
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ! [V_x] :
( ! [V_y] : ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_x,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f629]) ).
fof(f1597,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Equiv__Relations_Oequiv(X1,X4,X2)
| ~ c_in(c_Pair(X0,X3,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1596]) ).
fof(f1598,plain,
! [V_a,V_r,T_b,T_a] :
( ! [V_x] : ~ c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f630]) ).
fof(f1599,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X1,c_Relation_ORange(X4,X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f1598]) ).
fof(f1602,plain,
! [V_a,V_r,T_a,T_b] :
( ! [V_x] : ~ c_in(c_Pair(V_a,V_x,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
inference(miniscoping,[status(thm)],[f632]) ).
fof(f1603,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_in(c_Pair(X0,X4,X2,X3),X1,tc_prod(X2,X3))
| c_in(X0,c_Relation_ODomain(X1,X2,X3),X2) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
fof(f1610,plain,
! [T_a,V_r,V_A] :
( ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| ! [V_x] :
( ~ c_in(V_x,V_A,T_a)
| ! [V_xa] :
( ~ c_in(V_xa,V_A,T_a)
| V_x = V_xa
| c_in(c_Pair(V_x,V_xa,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_xa,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ) ),
inference(miniscoping,[status(thm)],[f636]) ).
fof(f1611,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Relation_Ototal__on(X4,X3,X2)
| ~ c_in(X0,X4,X2)
| X1 = X0
| ~ c_in(X1,X4,X2)
| c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f1610]) ).
fof(f1628,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [V_a_H,V_b_H] :
( V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ! [V_P] :
( ~ c_in(V_P,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ! [V_P_H] :
( ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ) ),
inference(miniscoping,[status(thm)],[f645]) ).
fof(f1629,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X3,X0,X1,X4,X2,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X2 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X0,X1,X4,X2,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(cnf_transformation,[status(thm)],[f1628]) ).
fof(f1630,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [V_a_H,V_b_H] :
( V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ! [V_P] :
( ~ c_in(V_P,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ! [V_P_H] :
( ~ c_in(V_P_H,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ) ),
inference(miniscoping,[status(thm)],[f646]) ).
fof(f1631,plain,
! [X0,X1,X2,X3,X4,X5] :
( X4 = X0
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X3,X5,X2,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X5,X2,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = X2
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1630]) ).
fof(f1632,plain,
! [X0] :
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f647]) ).
fof(f1633,plain,
! [X0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f648]) ).
fof(f1634,plain,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(cnf_transformation,[status(thm)],[f649]) ).
fof(f1635,plain,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(cnf_transformation,[status(thm)],[f650]) ).
fof(f1636,plain,
v_a_H____ != v_b____,
inference(cnf_transformation,[status(thm)],[f651]) ).
fof(f1637,plain,
v_a____ != v_b_H____,
inference(cnf_transformation,[status(thm)],[f652]) ).
fof(f1638,plain,
v_b_H____ != v_a_H____,
inference(cnf_transformation,[status(thm)],[f653]) ).
fof(f1639,plain,
v_b____ != v_a____,
inference(cnf_transformation,[status(thm)],[f654]) ).
fof(f1640,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f655]) ).
fof(f1641,plain,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f656]) ).
fof(f1672,definition,
( sQ0_spl
<=> c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1675,definition,
( sQ1_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1676,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f1675]) ).
fof(f1678,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1640,f1672,f1675]) ).
fof(f1679,plain,
( sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f1641,f1675,f1672]) ).
fof(f1692,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1597,f1633]) ).
fof(f1938,plain,
! [X0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1599,f1633]) ).
fof(f1992,plain,
! [X0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| v_b_H____ = v_a_H____ ),
inference(resolution,[status(thm)],[f1531,f1633]) ).
fof(f1993,plain,
( ~ sQ1_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_F,v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f1531,f1676]) ).
fof(f2001,definition,
( sQ2_spl
<=> v_b____ = v_a____ ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2002,plain,
( ~ sQ2_spl
| v_b____ = v_a____ ),
inference(component_clause,[status(thm)],[f2001]) ).
fof(f2004,definition,
( sQ3_spl
<=> c_Relation_Oantisym(hAPP(v_F,v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f2007,definition,
( sQ4_spl
<=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f2009,plain,
( sQ4_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2007]) ).
fof(f2010,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1993,f2001,f2004,f2007,f1675]) ).
fof(f2011,definition,
( sQ5_spl
<=> v_b_H____ = v_a_H____ ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f2012,plain,
( ~ sQ5_spl
| v_b_H____ = v_a_H____ ),
inference(component_clause,[status(thm)],[f2011]) ).
fof(f2014,definition,
! [X0] :
( sQ6_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f2015,plain,
! [X0] :
( ~ sQ6_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2014]) ).
fof(f2017,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1992,f2011,f2014]) ).
fof(f2019,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2012,f1638]) ).
fof(f2020,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f2019]) ).
fof(f2310,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b_H____ = v_a_H____
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1611,f2015]) ).
fof(f2312,plain,
! [X0,X1] :
( c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1611,f1938]) ).
fof(f2313,plain,
! [X0,X1,X2] :
( ~ c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1611,f1692]) ).
fof(f2315,plain,
! [X0,X1] :
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a_H____ = v_b_H____
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1611,f1632]) ).
fof(f2337,definition,
! [X0,X1] :
( sQ9_spl
<=> ( c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f2338,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2337]) ).
fof(f2340,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f2312,f2337,f2001]) ).
fof(f2346,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ( ~ c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2347,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2346]) ).
fof(f2349,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f2313,f2346,f2001]) ).
fof(f2350,definition,
! [X0,X1] :
( sQ12_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f2351,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2350]) ).
fof(f2353,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f2315,f2350,f2011]) ).
fof(f2354,definition,
! [X0,X1] :
( sQ13_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f2357,plain,
( ~ sQ6_spl
| sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f2310,f2354,f2011,f2014]) ).
fof(f2363,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2002,f1639]) ).
fof(f2364,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f2363]) ).
fof(f2399,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| v_a_H____ = v_b_H____
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2351,f1531]) ).
fof(f2400,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2351,f1599]) ).
fof(f2401,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2351,f1597]) ).
fof(f2402,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2405,plain,
( ~ sQ12_spl
| sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f2399,f2402,f2011,f2350]) ).
fof(f2406,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2338,f1531]) ).
fof(f2409,definition,
! [X0,X1] :
( sQ16_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2412,plain,
( ~ sQ9_spl
| sQ2_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f2406,f2409,f2001,f2337]) ).
fof(f2417,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2347,f1531]) ).
fof(f2420,definition,
! [X0,X1,X2] :
( sQ17_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2423,plain,
( ~ sQ11_spl
| sQ2_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f2417,f2420,f2001,f2346]) ).
fof(f2469,plain,
! [X0] :
( ~ sQ6_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1551,f2015]) ).
fof(f2470,plain,
! [X0] :
( ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1551,f1938]) ).
fof(f2471,plain,
! [X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1551,f1692]) ).
fof(f2473,plain,
! [X0] :
( ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1551,f1632]) ).
fof(f2498,plain,
! [X0] :
( ~ sQ6_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[status(thm)],[f2469,f1633]) ).
fof(f2534,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2473,f2351]) ).
fof(f2536,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b_H____ = v_a_H____
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2473,f1611]) ).
fof(f2537,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(duplicate_literals_removal,[status(thm)],[f2534]) ).
fof(f2538,definition,
! [X0,X1] :
( sQ19_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f2539,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2538]) ).
fof(f2541,plain,
( sQ5_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f2536,f2538,f2011]) ).
fof(f2543,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[status(thm)],[f2539,f1633]) ).
fof(f2547,plain,
! [X0] :
( ~ sQ6_spl
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2498,f1551]) ).
fof(f2548,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2498,f1611]) ).
fof(f2549,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f2550,plain,
! [X0,X1] :
( ~ sQ20_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2549]) ).
fof(f2552,plain,
( ~ sQ6_spl
| sQ2_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f2548,f2549,f2001,f2014]) ).
fof(f2565,plain,
! [X0,X1,X2] :
( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2471,f1611]) ).
fof(f2566,definition,
! [X0,X1,X2] :
( sQ21_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f2569,plain,
( sQ2_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f2565,f2566,f2001]) ).
fof(f2653,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2470,f1611]) ).
fof(f2655,definition,
! [X0,X1] :
( sQ22_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2658,plain,
( sQ2_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f2653,f2655,f2001]) ).
fof(f2734,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2547,f1611]) ).
fof(f2735,definition,
! [X0,X1] :
( sQ23_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2738,plain,
( ~ sQ6_spl
| sQ2_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f2734,f2735,f2001,f2014]) ).
fof(f2824,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2401,f1531]) ).
fof(f2827,definition,
! [X0,X1,X2] :
( sQ24_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2828,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X2,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2827]) ).
fof(f2830,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f2824,f2827,f2001,f2350]) ).
fof(f2835,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2400,f1531]) ).
fof(f2838,definition,
! [X0,X1] :
( sQ25_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f2839,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2838]) ).
fof(f2841,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f2835,f2838,f2001,f2350]) ).
fof(f2845,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2537,f1531]) ).
fof(f2850,definition,
! [X0,X1] :
( sQ26_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f2851,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2850]) ).
fof(f2853,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f2845,f2850,f2001,f2350]) ).
fof(f3144,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| v_b_H____ = v_a_H____
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2543,f1531]) ).
fof(f3147,definition,
! [X0,X1] :
( sQ27_spl
<=> ( ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f3150,plain,
( ~ sQ19_spl
| sQ5_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f3144,f3147,f2011,f2538]) ).
fof(f3457,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2550,f1531]) ).
fof(f3461,definition,
! [X0,X1] :
( sQ28_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f3464,plain,
( ~ sQ20_spl
| sQ2_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f3457,f3461,f2001,f2549]) ).
fof(f3583,plain,
! [X0,X1,X2] :
( ~ sQ26_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2851,f1611]) ).
fof(f3584,definition,
! [X0,X1,X2] :
( sQ29_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f3587,plain,
( ~ sQ26_spl
| sQ2_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f3583,f3584,f2001,f2850]) ).
fof(f3601,plain,
! [X0,X1] :
( ~ sQ12_spl
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1603,f2351]) ).
fof(f3607,plain,
! [X0] :
( c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1603,f1633]) ).
fof(f3646,plain,
! [X0] :
( c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3607,f1551]) ).
fof(f3647,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3607,f1611]) ).
fof(f3648,definition,
! [X0,X1] :
( sQ32_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f3649,plain,
! [X0,X1] :
( ~ sQ32_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f3648]) ).
fof(f3651,plain,
( sQ2_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f3647,f3648,f2001]) ).
fof(f3681,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3646,f1611]) ).
fof(f3682,definition,
! [X0,X1] :
( sQ33_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f3685,plain,
( sQ2_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f3681,f3682,f2001]) ).
fof(f3693,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3601,f1531]) ).
fof(f3696,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f3697,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f3696]) ).
fof(f3699,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f3693,f3696,f2001,f2350]) ).
fof(f3716,plain,
! [X0,X1] :
( ~ sQ32_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3649,f1531]) ).
fof(f3719,definition,
! [X0,X1] :
( sQ35_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f3722,plain,
( ~ sQ32_spl
| sQ2_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f3716,f3719,f2001,f3648]) ).
fof(f3772,plain,
! [X0,X1,X2,X3] :
( ~ sQ24_spl
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2828,f1611]) ).
fof(f3773,definition,
! [X0,X1,X2,X3] :
( sQ36_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f3776,plain,
( ~ sQ24_spl
| sQ2_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f3772,f3773,f2001,f2827]) ).
fof(f3925,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2839,f1611]) ).
fof(f3927,definition,
! [X0,X1,X2] :
( sQ37_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f3930,plain,
( ~ sQ25_spl
| sQ2_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f3925,f3927,f2001,f2838]) ).
fof(f3936,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3697,f1611]) ).
fof(f3937,definition,
! [X0,X1,X2] :
( sQ38_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f3940,plain,
( ~ sQ34_spl
| sQ2_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f3936,f3937,f2001,f3696]) ).
fof(f5259,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1527,f3601]) ).
fof(f5260,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1527,f2537]) ).
fof(f5261,plain,
! [X0,X1] :
( ~ sQ12_spl
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1527,f2400]) ).
fof(f5262,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1527,f2401]) ).
fof(f5263,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(hAPP(v_F,v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1527,f1676]) ).
fof(f5265,plain,
! [X0] :
( ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1527,f1633]) ).
fof(f5290,definition,
( sQ39_spl
<=> c_Wellfounded_Owf(hAPP(v_F,v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f5293,plain,
( ~ sQ1_spl
| ~ sQ39_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5263,f2007,f5290,f1675]) ).
fof(f5302,definition,
( sQ41_spl
<=> c_Relation_Osym(hAPP(v_F,v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f5313,plain,
( sQ4_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_F,v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f2009,f1551]) ).
fof(f5316,plain,
( sQ4_spl
| ~ sQ1_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f5313,f5302,f1675,f2007]) ).
fof(f5360,plain,
! [X0] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f5265,f1551]) ).
fof(f5361,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b_H____ = v_a_H____
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f5265,f1611]) ).
fof(f5362,plain,
! [X0] :
( ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[status(thm)],[f5360,f1632]) ).
fof(f5363,definition,
! [X0,X1] :
( sQ42_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f5366,plain,
( sQ5_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f5361,f5363,f2011]) ).
fof(f5705,plain,
! [X0] :
( ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f5362,f1633]) ).
fof(f5706,plain,
! [X0] :
( ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5362,f1551]) ).
fof(f5707,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a_H____ = v_b_H____
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5362,f1611]) ).
fof(f5708,plain,
! [X0] :
( ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literals_removal,[status(thm)],[f5706]) ).
fof(f5709,definition,
! [X0,X1] :
( sQ43_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b_H____,v_a_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f5712,plain,
( sQ5_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f5707,f5709,f2011]) ).
fof(f5716,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b_H____ = v_a_H____
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5708,f1611]) ).
fof(f5718,definition,
! [X0,X1] :
( sQ44_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f5721,plain,
( sQ5_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f5716,f5718,f2011]) ).
fof(f5727,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5260,f1611]) ).
fof(f5730,definition,
! [X0,X1,X2] :
( sQ45_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f5733,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f5727,f5730,f2001,f2350]) ).
fof(f5751,plain,
! [X0] :
( ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5705,f1551]) ).
fof(f5752,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5705,f1611]) ).
fof(f5753,definition,
! [X0,X1] :
( sQ46_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f5754,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f5753]) ).
fof(f5756,plain,
( sQ2_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f5752,f5753,f2001]) ).
fof(f5772,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5751,f1611]) ).
fof(f5773,definition,
! [X0,X1] :
( sQ47_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f5776,plain,
( sQ2_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f5772,f5773,f2001]) ).
fof(f5813,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5754,f1531]) ).
fof(f5817,definition,
! [X0,X1] :
( sQ48_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f5820,plain,
( ~ sQ46_spl
| sQ2_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f5813,f5817,f2001,f5753]) ).
fof(f5882,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5262,f1611]) ).
fof(f5883,definition,
! [X0,X1,X2,X3] :
( sQ49_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X2,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f5886,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f5882,f5883,f2001,f2350]) ).
fof(f5894,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5261,f1611]) ).
fof(f5896,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f5899,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f5894,f5896,f2001,f2350]) ).
fof(f5906,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5259,f1611]) ).
fof(f5908,definition,
! [X0,X1,X2] :
( sQ51_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f5911,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f5906,f5908,f2001,f2350]) ).
fof(f5992,plain,
! [X0,X1] :
( ~ sQ12_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1584,f2351]) ).
fof(f5999,plain,
! [X0] :
( ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1584,f1633]) ).
fof(f6109,plain,
! [X0] :
( ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f5999,f1551]) ).
fof(f6110,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5999,f1611]) ).
fof(f6111,definition,
! [X0,X1] :
( sQ56_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f6112,plain,
! [X0,X1] :
( ~ sQ56_spl
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f6111]) ).
fof(f6114,plain,
( sQ2_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f6110,f6111,f2001]) ).
fof(f6465,plain,
! [X0,X1] :
( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f6109,f1611]) ).
fof(f6467,definition,
! [X0,X1] :
( sQ57_spl
<=> ( ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Osym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f6470,plain,
( sQ2_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f6465,f6467,f2001]) ).
fof(f6558,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(paramodulation,[status(thm)],[f859,f690]) ).
fof(f6566,definition,
! [X0,X1] :
( sQ60_spl
<=> ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f6567,plain,
! [X0,X1] :
( ~ sQ60_spl
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(component_clause,[status(thm)],[f6566]) ).
fof(f6569,definition,
! [X2,X3] :
( sQ61_spl
<=> c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f6572,plain,
( sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f6558,f6566,f6569]) ).
fof(f6573,plain,
! [X0,X1] :
( ~ sQ60_spl
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(duplicate_literals_removal,[status(thm)],[f6567]) ).
fof(f6581,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Wellfounded_Owf(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5992,f1527]) ).
fof(f6583,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f5992,f1531]) ).
fof(f6586,definition,
! [X0,X1] :
( sQ62_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f6587,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f6586]) ).
fof(f6589,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f6583,f6586,f2001,f2350]) ).
fof(f6607,plain,
! [X0,X1] :
( ~ sQ56_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f6112,f1531]) ).
fof(f6611,definition,
! [X0,X1] :
( sQ63_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X1,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f6614,plain,
( ~ sQ56_spl
| sQ2_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f6607,f6611,f2001,f6111]) ).
fof(f6620,plain,
( ~ sQ60_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f678,f6573]) ).
fof(f6635,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f6620]) ).
fof(f6900,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f6581,f1611]) ).
fof(f6902,definition,
! [X0,X1,X2] :
( sQ64_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f6905,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f6900,f6902,f2001,f2350]) ).
fof(f6992,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f6587,f1611]) ).
fof(f6994,definition,
! [X0,X1,X2] :
( sQ65_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f6997,plain,
( ~ sQ62_spl
| sQ2_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f6992,f6994,f2001,f6586]) ).
fof(f7417,plain,
! [X0,X1,X2,X3] :
( ~ sQ62_spl
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f6587]) ).
fof(f7418,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f6581]) ).
fof(f7419,plain,
! [X0,X1,X2] :
( ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f6109]) ).
fof(f7420,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5259]) ).
fof(f7421,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5261]) ).
fof(f7422,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ12_spl
| c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X4,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5262]) ).
fof(f7423,plain,
! [X0,X1,X2] :
( ~ c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5751]) ).
fof(f7424,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5260]) ).
fof(f7425,plain,
! [X0,X1,X2,X3] :
( ~ sQ34_spl
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f3697]) ).
fof(f7426,plain,
! [X0,X1,X2,X3] :
( ~ sQ25_spl
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2839]) ).
fof(f7427,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ24_spl
| c_in(v_b_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X4,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2828]) ).
fof(f7428,plain,
! [X0,X1,X2] :
( c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f3646]) ).
fof(f7429,plain,
! [X0,X1,X2,X3] :
( ~ sQ26_spl
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2851]) ).
fof(f7430,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2547]) ).
fof(f7431,plain,
! [X0,X1,X2] :
( ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2470]) ).
fof(f7432,plain,
! [X0,X1,X2,X3] :
( ~ c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_b____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2471]) ).
fof(f7437,plain,
! [X0,X1,X2] :
( ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5999]) ).
fof(f7438,plain,
! [X0,X1,X2] :
( ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f5705]) ).
fof(f7439,plain,
! [X0,X1,X2] :
( c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f3607]) ).
fof(f7440,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f2498]) ).
fof(f7441,plain,
! [X0,X1,X2] :
( c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f1938]) ).
fof(f7442,plain,
! [X0,X1,X2,X3] :
( ~ c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f1631,f1692]) ).
fof(f7457,definition,
( sQ67_spl
<=> c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f7459,plain,
( sQ67_spl
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(component_clause,[status(thm)],[f7457]) ).
fof(f7465,definition,
! [X0,X1,X2] :
( sQ69_spl
<=> ( ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f7468,definition,
( sQ70_spl
<=> c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f7470,plain,
( sQ70_spl
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(component_clause,[status(thm)],[f7468]) ).
fof(f7471,plain,
( ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f7431,f7465,f7468,f2001,f2007]) ).
fof(f7476,definition,
! [X0,X1,X2,X3] :
( sQ72_spl
<=> ( ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f7479,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f7420,f7476,f7468,f2001,f2007,f2350]) ).
fof(f7480,definition,
! [X0,X1,X2,X3] :
( sQ73_spl
<=> ( ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f7483,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f7418,f7480,f7468,f2001,f2007,f2350]) ).
fof(f7484,definition,
! [X0,X1,X2] :
( sQ74_spl
<=> ( ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f7487,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f7438,f7484,f7468,f2001,f1675]) ).
fof(f7488,definition,
! [X0,X1,X2] :
( sQ75_spl
<=> ( c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f7491,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f7439,f7488,f7468,f2001,f1675]) ).
fof(f7492,definition,
! [X0,X1,X2,X3] :
( sQ76_spl
<=> ( ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f7495,plain,
( ~ sQ34_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f7425,f7492,f7468,f2001,f2007,f3696]) ).
fof(f7500,definition,
! [X0,X1,X2,X3,X4] :
( sQ78_spl
<=> ( c_in(v_b_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X4,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f7503,plain,
( ~ sQ24_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f7427,f7500,f7468,f2001,f2007,f2827]) ).
fof(f7504,definition,
! [X0,X1,X2,X3,X4] :
( sQ79_spl
<=> ( c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X4,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f7507,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f7422,f7504,f7468,f2001,f2007,f2350]) ).
fof(f7508,definition,
! [X0,X1,X2] :
( sQ80_spl
<=> ( c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f7511,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f7441,f7508,f7468,f2001,f1675]) ).
fof(f7512,definition,
! [X0,X1,X2] :
( sQ81_spl
<=> ( ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f7515,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f7430,f7512,f7468,f2001,f2007,f2014]) ).
fof(f7520,definition,
! [X0,X1,X2,X3] :
( sQ83_spl
<=> ( ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f7523,plain,
( ~ sQ62_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f7417,f7520,f7468,f2001,f2007,f6586]) ).
fof(f7524,definition,
! [X0,X1,X2] :
( sQ84_spl
<=> ( ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f7527,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f7437,f7524,f7468,f2001,f1675]) ).
fof(f7528,definition,
! [X0,X1,X2,X3] :
( sQ85_spl
<=> ( ~ c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f7531,plain,
( ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f7432,f7528,f7468,f2001,f2007]) ).
fof(f7532,definition,
! [X0,X1,X2] :
( sQ86_spl
<=> ( ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f7535,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f7440,f7532,f7468,f2001,f1675,f2014]) ).
fof(f7536,definition,
! [X0,X1,X2,X3] :
( sQ87_spl
<=> ( ~ c_Equiv__Relations_Oequiv(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f7539,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f7442,f7536,f7468,f2001,f1675]) ).
fof(f7541,definition,
! [X0,X1,X2] :
( sQ88_spl
<=> ( ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f7544,plain,
( ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f7419,f7541,f7468,f2001,f2007]) ).
fof(f7545,definition,
! [X0,X1,X2] :
( sQ89_spl
<=> ( ~ c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f7548,plain,
( ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f7423,f7545,f7468,f2001,f2007]) ).
fof(f7549,definition,
! [X0,X1,X2,X3] :
( sQ90_spl
<=> ( c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f7552,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f7421,f7549,f7468,f2001,f2007,f2350]) ).
fof(f7553,definition,
! [X0,X1,X2,X3] :
( sQ91_spl
<=> ( ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f7556,plain,
( ~ sQ26_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f7429,f7553,f7468,f2001,f2007,f2850]) ).
fof(f7557,definition,
! [X0,X1,X2,X3] :
( sQ92_spl
<=> ( ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f7560,plain,
( ~ sQ25_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f7426,f7557,f7468,f2001,f2007,f2838]) ).
fof(f7561,definition,
! [X0,X1,X2,X3] :
( sQ93_spl
<=> ( ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f7564,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f7424,f7561,f7468,f2001,f2007,f2350]) ).
fof(f7565,definition,
! [X0,X1,X2] :
( sQ94_spl
<=> ( c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = X0
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P____,X2,v_b____,X0,v_a____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f7568,plain,
( ~ sQ4_spl
| sQ2_spl
| ~ sQ70_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f7428,f7565,f7468,f2001,f2007]) ).
fof(f7574,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7459,f1634]) ).
fof(f7575,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f7574]) ).
fof(f7576,plain,
( sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7470,f1635]) ).
fof(f7577,plain,
sQ70_spl,
inference(contradiction_clause,[status(thm)],[f7576]) ).
fof(f7608,plain,
! [X0,X1,X2,X3] :
( ~ sQ56_spl
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f6112]) ).
fof(f7609,plain,
! [X0,X1,X2,X3] :
( ~ sQ46_spl
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f5754]) ).
fof(f7610,plain,
! [X0,X1,X2,X3] :
( ~ sQ32_spl
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f3649]) ).
fof(f7611,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f2550]) ).
fof(f7612,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ11_spl
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X4,hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f2347]) ).
fof(f7613,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f2338]) ).
fof(f7620,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_b_H____
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = v_b_H____
| X1 = v_a_H____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f2543]) ).
fof(f7621,plain,
! [X0,X1,X2] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b_H____
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = v_b_H____
| X1 = v_a_H____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f1629,f1633]) ).
fof(f7634,definition,
! [X0,X1,X2,X3,X4] :
( sQ97_spl
<=> ( ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X4,hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X4,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f7637,plain,
( ~ sQ11_spl
| sQ4_spl
| sQ2_spl
| sQ97_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7612,f7468,f7634,f2001,f2007,f2346]) ).
fof(f7638,definition,
! [X0,X1,X2,X3] :
( sQ98_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oantisym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f7641,plain,
( ~ sQ20_spl
| sQ4_spl
| sQ2_spl
| sQ98_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7611,f7468,f7638,f2001,f2007,f2549]) ).
fof(f7642,definition,
! [X0,X1,X2] :
( sQ99_spl
<=> ( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b_H____
| X1 = v_a_H____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f7643,plain,
! [X0,X1,X2] :
( ~ sQ99_spl
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b_H____ = X1
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_a_H____ = X0 ),
inference(component_clause,[status(thm)],[f7642]) ).
fof(f7645,plain,
( sQ0_spl
| sQ5_spl
| sQ99_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f7621,f7457,f7642,f2011,f1672]) ).
fof(f7650,definition,
! [X0,X1,X2,X3] :
( sQ101_spl
<=> ( ~ c_in(v_b_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_b_H____
| X1 = v_a_H____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f7653,plain,
( ~ sQ19_spl
| sQ0_spl
| sQ5_spl
| sQ101_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f7620,f7457,f7650,f2011,f1672,f2538]) ).
fof(f7654,definition,
! [X0,X1,X2,X3] :
( sQ102_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,c_Relation_ORange(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f7657,plain,
( ~ sQ9_spl
| sQ4_spl
| sQ2_spl
| sQ102_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7613,f7468,f7654,f2001,f2007,f2337]) ).
fof(f7658,definition,
! [X0,X1,X2,X3] :
( sQ103_spl
<=> ( ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Relation_ODomain(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f7661,plain,
( ~ sQ32_spl
| sQ4_spl
| sQ2_spl
| sQ103_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7610,f7468,f7658,f2001,f2007,f3648]) ).
fof(f7668,definition,
! [X0,X1,X2,X3] :
( sQ105_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Osym(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Wellfounded_Owf(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f7671,plain,
( ~ sQ46_spl
| sQ4_spl
| sQ2_spl
| sQ105_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7609,f7468,f7668,f2001,f2007,f5753]) ).
fof(f7676,definition,
! [X0,X1,X2,X3] :
( sQ107_spl
<=> ( ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,c_Wellfounded_Oacc(hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____
| X1 = v_b____
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P____,X0,v_b____,X1,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f7679,plain,
( ~ sQ56_spl
| sQ4_spl
| sQ2_spl
| sQ107_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f7608,f7468,f7676,f2001,f2007,f6111]) ).
fof(f7754,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Equiv__Relations_Oequiv(X4,c_Relation_Oconverse(X3,X2,X2),X2)
| c_in(X1,X4,X2)
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(resolution,[status(thm)],[f1508,f1597]) ).
fof(f7766,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_Oconverse(hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7754,f2351]) ).
fof(f7774,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7754,f1633]) ).
fof(f7923,definition,
( sQ111_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f7924,plain,
( ~ sQ111_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f7923]) ).
fof(f7926,definition,
( sQ112_spl
<=> v_b____ = v_a_H____ ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f7927,plain,
( ~ sQ112_spl
| v_b____ = v_a_H____ ),
inference(component_clause,[status(thm)],[f7926]) ).
fof(f7929,definition,
( sQ113_spl
<=> v_b_H____ = v_a____ ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f7930,plain,
( ~ sQ113_spl
| v_b_H____ = v_a____ ),
inference(component_clause,[status(thm)],[f7929]) ).
fof(f7932,definition,
( sQ114_spl
<=> c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f7933,plain,
( ~ sQ114_spl
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f7932]) ).
fof(f7934,plain,
( sQ114_spl
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f7932]) ).
fof(f7984,plain,
( sQ114_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f7934,f1633]) ).
fof(f7985,plain,
( sQ114_spl
| v_b_H____ = v_a____
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = v_a_H____
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b____ = v_a_H____
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f7934,f1631]) ).
fof(f7999,plain,
( sQ114_spl
| sQ113_spl
| ~ sQ0_spl
| sQ5_spl
| ~ sQ70_spl
| sQ1_spl
| sQ111_spl
| ~ sQ67_spl
| sQ112_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f7985,f2001,f7926,f7457,f7923,f1675,f7468,f2011,f1672,f7929,f7932]) ).
fof(f8001,plain,
( ~ sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7930,f1637]) ).
fof(f8002,plain,
~ sQ113_spl,
inference(contradiction_clause,[status(thm)],[f8001]) ).
fof(f8003,plain,
( ~ sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7927,f1636]) ).
fof(f8004,plain,
~ sQ112_spl,
inference(contradiction_clause,[status(thm)],[f8003]) ).
fof(f8024,plain,
! [X0,X1,X2] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hAPP(X1,v_a_H____) = hAPP(X1,v_b_H____)
| ~ c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X0),X1,tc_Arrow__Order__Mirabelle_Oalt,X2) ),
inference(resolution,[status(thm)],[f1533,f1633]) ).
fof(f8547,plain,
( sQ114_spl
| ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7984,f7924]) ).
fof(f8548,plain,
( sQ114_spl
| ~ sQ111_spl ),
inference(contradiction_clause,[status(thm)],[f8547]) ).
fof(f8610,plain,
! [X0,X1,X2,X3,X4] :
( v_b____ = X1
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,X1,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X2 = v_a____
| X1 = X2
| hAPP(X3,v_a_H____) = hAPP(X3,v_b_H____)
| ~ c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,X1,v_b____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,X4) ),
inference(resolution,[status(thm)],[f8024,f1631]) ).
fof(f8612,plain,
! [X0,X1,X2,X3] :
( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hAPP(X1,v_a_H____) = hAPP(X1,v_b_H____)
| ~ c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X0),X1,tc_Arrow__Order__Mirabelle_Oalt,X2) ),
inference(resolution,[status(thm)],[f8024,f1611]) ).
fof(f8613,definition,
! [X0,X1,X2,X3,X4] :
( sQ128_spl
<=> ( v_b____ = X1
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,X1,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = v_a____
| X1 = X2
| hAPP(X3,v_a_H____) = hAPP(X3,v_b_H____)
| ~ c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X0,v_a____,X1,v_b____,X2)),X3,tc_Arrow__Order__Mirabelle_Oalt,X4) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f8616,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f8610,f8613,f7468,f2001,f1675]) ).
fof(f8617,definition,
! [X0,X1,X2,X3] :
( sQ129_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| hAPP(X1,v_a_H____) = hAPP(X1,v_b_H____)
| ~ c_Equiv__Relations_Ocongruent(hAPP(v_P_H____,X0),X1,tc_Arrow__Order__Mirabelle_Oalt,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f8620,plain,
( sQ2_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f8612,f8617,f2001]) ).
fof(f9001,plain,
( ~ sQ114_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f7933,f1632]) ).
fof(f9033,plain,
( ~ sQ99_spl
| v_b____ = v_a_H____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b_H____ = v_a____
| v_a_H____ = v_b_H____
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b_H____ = v_a____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| v_a_H____ = v_b____ ),
inference(resolution,[status(thm)],[f7643,f1631]) ).
fof(f9035,plain,
! [X0,X1,X2,X3] :
( ~ sQ99_spl
| ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f7643,f1611]) ).
fof(f9036,definition,
( sQ153_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f9038,plain,
( sQ153_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f9036]) ).
fof(f9039,definition,
( sQ154_spl
<=> c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f9040,plain,
( ~ sQ154_spl
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f9039]) ).
fof(f9042,plain,
( ~ sQ99_spl
| ~ sQ67_spl
| sQ0_spl
| sQ154_spl
| sQ5_spl
| ~ sQ70_spl
| sQ113_spl
| ~ sQ1_spl
| ~ sQ153_spl
| sQ2_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f9033,f7926,f2001,f9036,f1675,f7929,f7468,f2011,f9039,f1672,f7457,f7642]) ).
fof(f9043,definition,
! [X0,X1,X2,X3] :
( sQ155_spl
<=> ( ~ c_Relation_Ototal__on(X3,hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X3,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_a_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f9046,plain,
( ~ sQ99_spl
| sQ2_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f9035,f9043,f2001,f7642]) ).
fof(f9187,plain,
( ~ sQ114_spl
| v_a_H____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| v_b_H____ = v_a____
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = v_b_H____
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f9001,f1629]) ).
fof(f9200,plain,
( sQ112_spl
| sQ1_spl
| sQ2_spl
| sQ113_spl
| ~ sQ67_spl
| ~ sQ0_spl
| sQ5_spl
| ~ sQ114_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f9187,f7468,f7932,f2011,f1672,f7457,f7929,f2001,f1675,f7926]) ).
fof(f9355,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_Oconverse(hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7766,f1531]) ).
fof(f9362,definition,
! [X0,X1,X2] :
( sQ157_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_Oconverse(hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(X0,hAPP(v_P_H____,X2),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a_H____,X0,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_a_H____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f9365,plain,
( ~ sQ12_spl
| sQ2_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f9355,f9362,f2001,f2350]) ).
fof(f9374,plain,
! [X0,X1,X2,X3] :
( v_b____ = X2
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X3 = v_a____
| X2 = X3
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,X2,v_b____,X3)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7774,f1631]) ).
fof(f9376,plain,
! [X0,X1,X2] :
( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7774,f1611]) ).
fof(f9377,definition,
! [X0,X1,X2] :
( sQ158_spl
<=> ( ~ c_Relation_Ototal__on(X2,hAPP(v_P____,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,X2,tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(hAPP(v_P_H____,X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f9380,plain,
( sQ2_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f9376,f9377,f2001]) ).
fof(f9381,definition,
! [X0,X1,X2,X3] :
( sQ159_spl
<=> ( v_b____ = X2
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_a____
| X2 = X3
| ~ c_Equiv__Relations_Oequiv(X0,c_Relation_Oconverse(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,X1,v_a____,X2,v_b____,X3)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b_H____,X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f9384,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ70_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f9374,f9381,f7468,f2001,f1675]) ).
fof(f10480,plain,
( sQ153_spl
| v_b____ = v_a_H____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_b_H____ = v_a____
| v_a_H____ = v_b_H____ ),
inference(resolution,[status(thm)],[f9038,f1631]) ).
fof(f10501,plain,
( sQ153_spl
| sQ112_spl
| ~ sQ1_spl
| sQ2_spl
| ~ sQ67_spl
| sQ0_spl
| sQ154_spl
| ~ sQ70_spl
| sQ113_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f10480,f2011,f7929,f7468,f9039,f1672,f7457,f2001,f1675,f7926,f9036]) ).
fof(f10547,plain,
( ~ sQ154_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f9040,f1632]) ).
fof(f10548,plain,
( ~ sQ154_spl
| v_a____ = v_b_H____
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = v_b_H____
| v_b____ = v_a_H____
| ~ c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(resolution,[status(thm)],[f9040,f1629]) ).
fof(f10568,plain,
( ~ sQ154_spl
| sQ153_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10547,f9038]) ).
fof(f10569,plain,
( ~ sQ154_spl
| sQ153_spl ),
inference(contradiction_clause,[status(thm)],[f10568]) ).
fof(f10570,plain,
( ~ sQ154_spl
| sQ113_spl
| sQ0_spl
| sQ5_spl
| sQ112_spl
| ~ sQ70_spl
| ~ sQ1_spl
| sQ2_spl
| ~ sQ153_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f10548,f7457,f9036,f2001,f1675,f7468,f7926,f2011,f1672,f7929,f9039]) ).
fof(f10576,plain,
$false,
inference(sat_refutation,[status(thm)],[f1678,f1679,f2010,f2017,f2020,f2340,f2349,f2353,f2357,f2364,f2405,f2412,f2423,f2541,f2552,f2569,f2658,f2738,f2830,f2841,f2853,f3150,f3464,f3587,f3651,f3685,f3699,f3722,f3776,f3930,f3940,f5293,f5316,f5366,f5712,f5721,f5733,f5756,f5776,f5820,f5886,f5899,f5911,f6114,f6470,f6572,f6589,f6614,f6635,f6905,f6997,f7471,f7479,f7483,f7487,f7491,f7495,f7503,f7507,f7511,f7515,f7523,f7527,f7531,f7535,f7539,f7544,f7548,f7552,f7556,f7560,f7564,f7568,f7575,f7577,f7637,f7641,f7645,f7653,f7657,f7661,f7671,f7679,f7999,f8002,f8004,f8548,f8616,f8620,f9042,f9046,f9200,f9365,f9380,f9384,f10501,f10569,f10570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT041-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 04:27:34 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.28/0.57 % Drodi V4.1.1
% 177.82/23.14 % Refutation found
% 177.82/23.14 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 177.82/23.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 167.17/24.37 % Elapsed time: 23.707100 seconds
% 167.17/24.37 % CPU time: 172.894489 seconds
% 167.17/24.37 % Total memory used: 1.104 GB
% 167.17/24.37 % Net memory used: 1.055 GB
%------------------------------------------------------------------------------