%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT066-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:06:52 PM UTC 2026
% Result : Unsatisfiable 134.76s 27.68s
% Output : CNFRefutation 134.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 83
% Syntax : Number of formulae : 309 ( 22 unt; 65 def)
% Number of atoms : 2746 (1183 equ)
% Maximal formula atoms : 28 ( 8 avg)
% Number of connectives : 3486 (1049 ~;2372 |; 0 &)
% ( 65 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 69 ( 67 usr; 66 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-6 aty)
% Number of variables : 842 ( 842 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [V_f,T_b,T_a] : c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f649,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f650,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f653,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f655,axiom,
! [V_x,V_S,T_a] :
( ~ hBOOL(hAPP(V_S,V_x))
| c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f656,axiom,
! [V_S,V_x,T_a] :
( ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f657,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f659,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f660,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f663,axiom,
! [V_a,V_b,V_P,V_a_H,V_b_H,V_P_H] :
( 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_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f664,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),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),v_F(V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f665,axiom,
! [V_a,V_b,V_P,V_a_H,V_b_H,V_P_H] :
( 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_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f666,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),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),v_F(V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f667,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f668,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f669,negated_conjecture,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f670,negated_conjecture,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f708,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f809,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)],[f80]) ).
fof(f810,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X3,X1,X0,X2)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X1 ),
inference(cnf_transformation,[status(thm)],[f809]) ).
fof(f1658,plain,
v_b____ != v_a____,
inference(cnf_transformation,[status(thm)],[f649]) ).
fof(f1659,plain,
v_a_H____ != v_b_H____,
inference(cnf_transformation,[status(thm)],[f650]) ).
fof(f1664,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_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(cnf_transformation,[status(thm)],[f653]) ).
fof(f1666,plain,
! [V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| ! [T_a] : c_in(V_x,V_S,T_a) ),
inference(miniscoping,[status(thm)],[f655]) ).
fof(f1667,plain,
! [X0,X1,X2] :
( c_in(X1,X0,X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1666]) ).
fof(f1668,plain,
! [V_S,V_x] :
( ! [T_a] : ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
inference(miniscoping,[status(thm)],[f656]) ).
fof(f1669,plain,
! [X0,X1,X2] :
( ~ c_in(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1668]) ).
fof(f1670,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_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(cnf_transformation,[status(thm)],[f657]) ).
fof(f1672,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)],[f659]) ).
fof(f1673,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)],[f660]) ).
fof(f1676,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_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ) ),
inference(miniscoping,[status(thm)],[f663]) ).
fof(f1677,plain,
! [X0,X1,X2,X3,X4,X5] :
( X5 = X4
| X5 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X0,X3,X2,X4,X1,X5)),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)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,X3,X2,X4,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ 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)],[f1676]) ).
fof(f1678,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),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),v_F(V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ) ),
inference(miniscoping,[status(thm)],[f664]) ).
fof(f1679,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X1
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ 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(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X5,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,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 = X2
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1678]) ).
fof(f1680,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_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ) ),
inference(miniscoping,[status(thm)],[f665]) ).
fof(f1681,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,X2,X4,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = 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(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X5 = X4
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X0,X2,X4,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ 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)],[f1680]) ).
fof(f1682,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),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),v_F(V_P_H),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ) ),
inference(miniscoping,[status(thm)],[f666]) ).
fof(f1683,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X5,X2,X3,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ 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(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__CHAINED__1(X5,X2,X3,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X0
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),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)))
| X1 = X0
| X3 = X4
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f1682]) ).
fof(f1684,plain,
v_b____ != v_a_H____,
inference(cnf_transformation,[status(thm)],[f667]) ).
fof(f1685,plain,
v_a____ != v_b_H____,
inference(cnf_transformation,[status(thm)],[f668]) ).
fof(f1686,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f669]) ).
fof(f1687,plain,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f670]) ).
fof(f1721,definition,
( sQ0_spl
<=> c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(f1722,plain,
( ~ sQ0_spl
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f1721]) ).
fof(f1724,definition,
( sQ1_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(f1725,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f1724]) ).
fof(f1727,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1686,f1721,f1724]) ).
fof(f1728,plain,
( sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f1687,f1724,f1721]) ).
fof(f1762,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( v_a____ = X1
| 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(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____,X2,v_a____,X0,v_b____,X1)),tc_prod(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)))
| X1 = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1763,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ 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,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__CHAINED__1(v_P____,X1,v_a____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| v_b____ = X2
| c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(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____,v_sko__CHAINED__1(v_P____,X1,v_a____,X2,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(component_clause,[status(thm)],[f1762]) ).
fof(f1765,definition,
( sQ3_spl
<=> v_a____ = v_b____ ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1766,plain,
( ~ sQ3_spl
| v_a____ = v_b____ ),
inference(component_clause,[status(thm)],[f1765]) ).
fof(f1768,definition,
( sQ4_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,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1770,plain,
( sQ4_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)],[f1768]) ).
fof(f1772,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| v_a_H____ = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,X0,v_b_H____,X1)),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)))
| 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____,X2,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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)))
| X1 = X0
| v_a_H____ = v_b_H____
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1722,f1683]) ).
fof(f1773,definition,
! [X0,X1,X2] :
( sQ5_spl
<=> ( v_a_H____ = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,X0,v_b_H____,X1)),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_H____,X2,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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)))
| X1 = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1774,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,X2,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| 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),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b_H____ ),
inference(component_clause,[status(thm)],[f1773]) ).
fof(f1776,definition,
( sQ6_spl
<=> v_a_H____ = v_b_H____ ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1777,plain,
( ~ sQ6_spl
| v_a_H____ = v_b_H____ ),
inference(component_clause,[status(thm)],[f1776]) ).
fof(f1779,definition,
( sQ7_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,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1781,plain,
( sQ7_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)],[f1779]) ).
fof(f1782,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1772,f1773,f1776,f1779,f1721]) ).
fof(f1783,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1777,f1659]) ).
fof(f1784,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f1783]) ).
fof(f1785,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1770,f1673]) ).
fof(f1786,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1785]) ).
fof(f1923,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X1,X3)
| ~ c_in(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1667,f1669]) ).
fof(f1925,plain,
! [X0,X1] :
( 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_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),X1) ),
inference(resolution,[status(thm)],[f1923,f1664]) ).
fof(f1927,plain,
! [X0,X1] :
( ~ 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),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)) ),
inference(resolution,[status(thm)],[f1923,f1670]) ).
fof(f2031,plain,
! [X0,X1,X2] :
( ~ sQ1_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____,X1,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = 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(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X1
| v_b____ = v_a____
| 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____,X1,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ 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)],[f1681,f1725]) ).
fof(f2033,definition,
! [X0,X1,X2] :
( sQ8_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____,X1,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = 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(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X1
| 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____,X1,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f2034,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| v_a____ = X2
| ~ 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(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,X2,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = 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(X0,v_P____,X1,v_a____,X2,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2033]) ).
fof(f2036,plain,
( ~ sQ1_spl
| sQ3_spl
| sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2031,f1768,f2033,f1765,f1724]) ).
fof(f2037,plain,
! [X0,X1,X2] :
( ~ sQ0_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(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 = 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(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| v_b_H____ = v_a_H____
| 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
| ~ 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)],[f1722,f1681]) ).
fof(f2040,definition,
! [X0,X1,X2] :
( sQ9_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(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 = 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(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| 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 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f2041,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),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(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(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))
| ~ 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)))
| X1 = v_b_H____
| X1 = X0
| v_a_H____ = X0 ),
inference(component_clause,[status(thm)],[f2040]) ).
fof(f2043,plain,
( ~ sQ0_spl
| sQ6_spl
| sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2037,f1779,f2040,f1776,f1721]) ).
fof(f2044,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1766,f1658]) ).
fof(f2045,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f2044]) ).
fof(f2046,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1781,f1672]) ).
fof(f2047,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f2046]) ).
fof(f2228,definition,
! [X2] :
( sQ11_spl
<=> c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2346,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| v_b____ = v_a____
| v_b____ = X2
| X1 = v_a____
| ~ 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(X0,v_P____,X2,v_a____,X1,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)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X2,v_a____,X1,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ 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(resolution,[status(thm)],[f1677,f1725]) ).
fof(f2348,definition,
! [X0,X1,X2] :
( sQ12_spl
<=> ( v_b____ = X2
| X1 = v_a____
| ~ 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(X0,v_P____,X2,v_a____,X1,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X2,v_a____,X1,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ 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))) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f2349,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,X1,v_a____,X2,v_b____)),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)))
| v_a____ = X2
| X2 = 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(X0,v_P____,X1,v_a____,X2,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2348]) ).
fof(f2351,plain,
( ~ sQ1_spl
| sQ3_spl
| ~ sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f2346,f2348,f1768,f1765,f1724]) ).
fof(f2352,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____,v_sko__CHAINED__1(v_P_H____,v_P____,X0,v_a____,X1,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a____
| X0 = v_b____
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X0,v_a____,X1,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2349,f1672]) ).
fof(f2356,plain,
! [X0,X1,X2] :
( ~ sQ12_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____,X0,v_a____,X1,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X0,v_a____,X1,v_b____)),X2)
| v_a____ = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[f2352,f1923]) ).
fof(f2357,definition,
( sQ13_spl
<=> v_a____ = v_b_H____ ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f2358,plain,
( ~ sQ13_spl
| v_a____ = v_b_H____ ),
inference(component_clause,[status(thm)],[f2357]) ).
fof(f2360,definition,
( sQ14_spl
<=> v_a_H____ = v_b____ ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f2361,plain,
( ~ sQ14_spl
| v_a_H____ = v_b____ ),
inference(component_clause,[status(thm)],[f2360]) ).
fof(f2363,definition,
( sQ15_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,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2366,definition,
! [X0] :
( sQ16_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____)),X0) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2367,plain,
! [X0] :
( ~ sQ16_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____)),X0) ),
inference(component_clause,[status(thm)],[f2366]) ).
fof(f2371,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| v_b_H____ = v_a_H____
| v_b_H____ = X2
| X1 = v_a_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(X0,v_P_H____,X2,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)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ 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(resolution,[status(thm)],[f1722,f1677]) ).
fof(f2374,definition,
! [X0,X1,X2] :
( sQ17_spl
<=> ( v_b_H____ = X2
| X1 = v_a_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(X0,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ 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))) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2375,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| X1 = v_a_H____
| ~ 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(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(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(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)))
| X1 = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b_H____ ),
inference(component_clause,[status(thm)],[f2374]) ).
fof(f2377,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ7_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f2371,f2374,f1779,f1776,f1721]) ).
fof(f2390,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
inference(paramodulation,[status(thm)],[f708,f810]) ).
fof(f2391,definition,
! [X1] :
( sQ18_spl
<=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f2392,plain,
! [X0] :
( ~ sQ18_spl
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
inference(component_clause,[status(thm)],[f2391]) ).
fof(f2394,plain,
( sQ18_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f2390,f2228,f2391]) ).
fof(f2403,plain,
( ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2392]) ).
fof(f2404,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f2403]) ).
fof(f2467,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| X0 = v_b____
| X1 = v_a____
| ~ 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____,X0,v_a____,X1,v_b____)),X3)
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X0,v_a____,X1,v_b____)),X2) ),
inference(resolution,[status(thm)],[f2356,f1927]) ).
fof(f2468,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P____,v_sko__CHAINED__1(v_P_H____,v_P____,X0,v_a____,X1,v_b____)),X3)
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X0,v_a____,X1,v_b____)),X2)
| v_b____ = X0
| X1 = v_a____
| X0 = X1 ),
inference(resolution,[status(thm)],[f2356,f1923]) ).
fof(f2544,plain,
! [X0,X1] :
( ~ sQ17_spl
| X1 = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_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____ ),
inference(resolution,[status(thm)],[f2375,f1672]) ).
fof(f2545,plain,
! [X0,X1] :
( ~ sQ17_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____,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_P____,v_sko__CHAINED__1(v_P____,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_b_H____ = X1
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f2375,f1673]) ).
fof(f2563,plain,
( ~ sQ8_spl
| ~ sQ16_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)))
| 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))
| v_a____ = v_b_H____
| v_b____ = v_a_H____
| 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),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2367,f2034]) ).
fof(f2566,definition,
( sQ25_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,[sQ25_spl])],[split_symbol_definition]) ).
fof(f2567,plain,
( ~ sQ25_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)],[f2566]) ).
fof(f2568,plain,
( sQ25_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)],[f2566]) ).
fof(f2569,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ7_spl
| sQ25_spl
| sQ13_spl
| sQ14_spl
| sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f2563,f1721,f1776,f2360,f2357,f2566,f1779,f2366,f2033]) ).
fof(f2570,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2358,f1685]) ).
fof(f2571,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f2570]) ).
fof(f2572,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2361,f1684]) ).
fof(f2573,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f2572]) ).
fof(f2610,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ17_spl
| X0 = X1
| X0 = X4
| X3 = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X4,X1,X3,X0)),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)))
| c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X4,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ 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)))
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f2544,f1677]) ).
fof(f2611,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ17_spl
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X3,X1,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X4,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(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| X0 = X1
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X3,X1,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| ~ 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)))
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f2544,f1681]) ).
fof(f2612,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ17_spl
| X1 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X0,X3)),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)))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X0,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ c_in(X4,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 = X2
| X1 = X0
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f2544,f1683]) ).
fof(f2613,definition,
! [X0,X1,X2,X3,X4] :
( sQ26_spl
<=> ( X0 = X1
| X0 = X4
| X3 = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X4,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X4,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ 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)))
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f2614,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ26_spl
| X0 = X1
| X0 = X4
| X3 = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X4,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X4,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ 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)))
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(component_clause,[status(thm)],[f2613]) ).
fof(f2616,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f2610,f2613,f1779,f2374]) ).
fof(f2617,definition,
! [X0,X1,X2,X3,X4] :
( sQ27_spl
<=> ( c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X3,X1,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X4,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(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| X0 = X1
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X3,X1,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f2618,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ27_spl
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X3,X1,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X4,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(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| X0 = X1
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X3,X1,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(component_clause,[status(thm)],[f2617]) ).
fof(f2620,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f2611,f2617,f1779,f2374]) ).
fof(f2621,definition,
! [X0,X1,X2,X3,X4] :
( sQ28_spl
<=> ( X1 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X0,X3)),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_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X0,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ c_in(X4,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 = X2
| X1 = X0
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f2624,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f2612,f2621,f1779,f2374]) ).
fof(f2626,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ27_spl
| X1 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X3,X0,X4,X1)),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)))
| X1 = X0
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),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_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| X4 = X0
| X3 = X4
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X3,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f2618]) ).
fof(f2627,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ26_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_H____,X3,v_a_H____,X4,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)))
| X3 = X1
| X4 = v_a_H____
| X4 = X0
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X4,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X0,X3,X1,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X3
| X3 = v_b_H____
| ~ 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,X3,X1,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literals_removal,[status(thm)],[f2614]) ).
fof(f2632,plain,
! [X0] :
( ~ sQ17_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____)),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____,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_b_H____ = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = v_b____ ),
inference(resolution,[status(thm)],[f2545,f1927]) ).
fof(f2633,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| X1 = X0
| v_b_H____ = 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____,v_sko__CHAINED__1(v_P____,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(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),X2) ),
inference(resolution,[status(thm)],[f2545,f1923]) ).
fof(f2634,definition,
( sQ29_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,[sQ29_spl])],[split_symbol_definition]) ).
fof(f2636,plain,
( sQ29_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)],[f2634]) ).
fof(f2637,definition,
! [X0] :
( sQ30_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____)),X0) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f2638,plain,
! [X0] :
( ~ sQ30_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____)),X0) ),
inference(component_clause,[status(thm)],[f2637]) ).
fof(f2640,plain,
( ~ sQ17_spl
| sQ30_spl
| ~ sQ29_spl
| sQ3_spl
| sQ13_spl
| sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f2632,f2360,f1724,f2357,f1765,f2634,f2637,f2374]) ).
fof(f2642,plain,
! [X0,X1,X2,X3] :
( ~ sQ26_spl
| v_b_H____ = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X0
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| ~ 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_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f2627,f1672]) ).
fof(f2643,plain,
! [X0,X1,X2,X3] :
( ~ sQ26_spl
| X3 = X2
| X3 = X0
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| v_a_H____ = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X0,X3,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),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(resolution,[status(thm)],[f2627,f1673]) ).
fof(f2651,plain,
( ~ sQ9_spl
| ~ sQ30_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))
| ~ 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____ = v_a_H____
| v_b_H____ = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f2638,f2041]) ).
fof(f2653,plain,
( ~ sQ27_spl
| ~ sQ30_spl
| v_a_H____ = v_b_H____
| v_a_H____ = v_b____
| v_a_H____ = v_b_H____
| v_b____ = v_a____
| ~ 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_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_H____,v_a_H____,v_a_H____,v_b_H____,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_H____,v_P_H____,v_a_H____,v_a_H____,v_b_H____,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_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____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = v_a____
| v_a_H____ = v_b_H____ ),
inference(resolution,[status(thm)],[f2638,f2626]) ).
fof(f2655,definition,
( sQ31_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,[sQ31_spl])],[split_symbol_definition]) ).
fof(f2656,plain,
( ~ sQ31_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)],[f2655]) ).
fof(f2658,definition,
( sQ32_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_H____,v_a_H____,v_a_H____,v_b_H____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f2661,plain,
( ~ sQ27_spl
| ~ sQ30_spl
| sQ14_spl
| sQ3_spl
| ~ sQ4_spl
| ~ sQ32_spl
| sQ31_spl
| sQ1_spl
| sQ13_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2653,f1776,f2357,f1724,f2655,f2658,f1768,f1765,f2360,f2637,f2617]) ).
fof(f2663,plain,
( ~ sQ9_spl
| ~ sQ30_spl
| sQ31_spl
| ~ sQ4_spl
| sQ14_spl
| sQ13_spl
| sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f2651,f1765,f1724,f2357,f2360,f1768,f2655,f2637,f2040]) ).
fof(f2677,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ26_spl
| X2 = X3
| X2 = X6
| X5 = X3
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X6,X3,X5,X2)),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)))
| c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X6,X3,X5,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X4,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 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2642,f1677]) ).
fof(f2678,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ26_spl
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X5,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X3
| ~ c_in(X6,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(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X2 = X3
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X5,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| ~ 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)))
| X3 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2642,f1681]) ).
fof(f2679,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ26_spl
| X3 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X3,X4,X2,X5)),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)))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X3,X4,X2,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| ~ c_in(X6,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)))
| X5 = X4
| X3 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2642,f1683]) ).
fof(f2680,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ33_spl
<=> ( X2 = X3
| X2 = X6
| X5 = X3
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X6,X3,X5,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X6,X3,X5,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X4,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 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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,[sQ33_spl])],[split_symbol_definition]) ).
fof(f2681,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ33_spl
| X2 = X3
| X2 = X6
| X5 = X3
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X6,X3,X5,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X6,X3,X5,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X4,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 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2680]) ).
fof(f2683,plain,
( ~ sQ26_spl
| ~ sQ7_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f2677,f2680,f1779,f2613]) ).
fof(f2684,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ34_spl
<=> ( X3 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X3,X4,X2,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X3,X4,X2,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| ~ c_in(X6,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)))
| X5 = X4
| X3 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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,[sQ34_spl])],[split_symbol_definition]) ).
fof(f2687,plain,
( ~ sQ26_spl
| ~ sQ7_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f2679,f2684,f1779,f2613]) ).
fof(f2688,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ35_spl
<=> ( c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X5,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X3
| ~ c_in(X6,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(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X2 = X3
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X5,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X3 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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,[sQ35_spl])],[split_symbol_definition]) ).
fof(f2689,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ35_spl
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X5,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X3
| ~ c_in(X6,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(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X2 = X3
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X5,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X3 = X2
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ 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_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(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2688]) ).
fof(f2691,plain,
( ~ sQ26_spl
| ~ sQ7_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f2678,f2688,f1779,f2613]) ).
fof(f2692,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ35_spl
| X0 = X1
| X5 = X3
| X5 = X6
| c_in(c_Pair(X3,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X6,X3,X4,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X5,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X6,X3,X4,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X6
| c_in(c_Pair(X6,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X5,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X3
| X1 = X3
| 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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literals_removal,[status(thm)],[f2689]) ).
fof(f2694,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ33_spl
| X6 = X4
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X6,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X5,v_P_H____,X0,X6,X1,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X6,X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X2
| X1 = X6
| X0 = X4
| ~ 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(X5,v_sko__CHAINED__1(X5,v_P_H____,X0,X6,X1,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| v_a_H____ = X2
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f2681]) ).
fof(f2721,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ26_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)))
| c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_b____ = X1
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____
| v_b____ = X1
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| ~ 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_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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_a____ = v_b____
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f2643,f1763]) ).
fof(f2722,plain,
! [X0,X1,X2] :
( ~ sQ26_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____,X1,v_b____,X0)),X2)
| v_b____ = X1
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| ~ 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_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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_a____ = v_b____
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f2643,f1927]) ).
fof(f2723,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ26_spl
| X3 = X1
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X1,X0,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| v_a_H____ = X3
| X3 = X2
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X3,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_H____,v_P_H____,X1,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X1,X0,X3)),X4)
| X0 = X1 ),
inference(resolution,[status(thm)],[f2643,f1923]) ).
fof(f2724,definition,
! [X0,X1] :
( sQ36_spl
<=> ( c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_b____ = X1
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____
| v_b____ = X1
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| ~ 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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f2727,plain,
( ~ sQ2_spl
| ~ sQ26_spl
| ~ sQ7_spl
| sQ1_spl
| sQ3_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f2721,f2724,f1765,f1724,f1779,f2613,f1762]) ).
fof(f2728,definition,
! [X0,X1,X2] :
( sQ37_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____,X1,v_b____,X0)),X2)
| v_b____ = X1
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| ~ 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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f2729,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| ~ 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____,X1,v_b____,X0)),X2)
| X0 = v_a_H____
| X1 = v_b_H____
| v_a____ = X0 ),
inference(component_clause,[status(thm)],[f2728]) ).
fof(f2731,plain,
( ~ sQ26_spl
| sQ1_spl
| sQ3_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f2722,f2728,f1765,f1724,f2613]) ).
fof(f2794,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = v_a_H____
| v_a_H____ = v_b____
| 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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),X0) ),
inference(resolution,[status(thm)],[f2567,f2467]) ).
fof(f2796,definition,
! [X0] :
( sQ42_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____)),X0) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f2797,plain,
! [X0] :
( ~ sQ42_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____)),X0) ),
inference(component_clause,[status(thm)],[f2796]) ).
fof(f2799,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| sQ0_spl
| sQ6_spl
| sQ14_spl
| sQ13_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f2794,f2796,f2357,f2360,f1776,f1721,f2566,f2348]) ).
fof(f2826,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____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),X1)
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,v_a____,v_b_H____,v_b____)),X0)
| v_b____ = v_a_H____
| v_b_H____ = v_a____
| v_a_H____ = v_b_H____ ),
inference(resolution,[status(thm)],[f2468,f1925]) ).
fof(f2828,plain,
( ~ sQ12_spl
| sQ0_spl
| sQ16_spl
| sQ14_spl
| sQ13_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2826,f1776,f2357,f2360,f2366,f1721,f2348]) ).
fof(f3032,plain,
( ~ sQ25_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2567,f2797]) ).
fof(f3033,plain,
( ~ sQ25_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f3032]) ).
fof(f3042,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ26_spl
| X0 = X1
| X0 = X2
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X1,X3,X0)),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = 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_H____,X1,v_a_H____,X0,v_b_H____)),X4)
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f2643,f1923]) ).
fof(f3062,plain,
! [X0,X1,X2,X3] :
( ~ sQ26_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____,X1,v_a_H____,X0,v_b_H____)),X3)
| v_b_H____ = v_a_H____
| v_b_H____ = v_a_H____
| v_a_H____ = v_b_H____
| v_b_H____ = X1
| ~ 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_H____,v_a_H____,v_a_H____,v_b_H____,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_H____,v_P_H____,v_a_H____,v_a_H____,v_b_H____,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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),X2)
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f2723,f1925]) ).
fof(f3063,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ26_spl
| X3 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X0,X2,X1,X3)),X5)
| X2 = v_b_H____
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,X0,X2,X1,X3)),X4)
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2723,f1923]) ).
fof(f3064,definition,
! [X0,X1,X2,X3] :
( sQ50_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____,X1,v_a_H____,X0,v_b_H____)),X3)
| v_b_H____ = X1
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),X2)
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f3067,plain,
( ~ sQ26_spl
| sQ6_spl
| ~ sQ32_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f3062,f3064,f2658,f1776,f2613]) ).
fof(f3068,plain,
! [X0,X1,X2] :
( ~ sQ26_spl
| ~ sQ9_spl
| v_b_H____ = v_a_H____
| v_b_H____ = v_a_H____
| v_a_H____ = v_b_H____
| v_b_H____ = X1
| ~ 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_H____,v_a_H____,v_a_H____,v_b_H____,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_H____,v_P_H____,v_a_H____,v_a_H____,v_b_H____,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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),X2)
| X0 = v_a_H____
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),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_P____,v_sko__CHAINED__1(v_P____,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(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_H____
| X1 = X0
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f2041,f2723]) ).
fof(f3069,definition,
! [X0,X1,X2] :
( sQ51_spl
<=> ( v_b_H____ = X1
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),X2)
| X0 = v_a_H____
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),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_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b_H____
| X1 = X0
| v_a_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f3072,plain,
( ~ sQ26_spl
| ~ sQ9_spl
| sQ6_spl
| ~ sQ32_spl
| ~ sQ4_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f3068,f3069,f1768,f2658,f1776,f2040,f2613]) ).
fof(f3101,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| v_b_H____ = v_a_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____,X2,v_a_H____,X1,v_b_H____,X0)),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)))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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(v_P_H____,X2,v_a_H____,X1,v_b_H____,X0)),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
| X0 = X1
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f1679,f1722]) ).
fof(f3102,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ17_spl
| X3 = X1
| X3 = v_a_H____
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X3,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_H____,v_P_H____,X1,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b_H____
| X3 = X1
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X3,X0)),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)))
| c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,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 = X2
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[f1679,f2544]) ).
fof(f3104,definition,
! [X0,X1,X2,X3,X4] :
( sQ52_spl
<=> ( X3 = X1
| X3 = v_a_H____
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X3,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_H____,v_P_H____,X1,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b_H____
| X3 = X1
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,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 = X2
| X0 = X2
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f3105,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ52_spl
| X3 = X1
| X3 = v_a_H____
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X3,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_H____,v_P_H____,X1,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b_H____
| X3 = X1
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X1,X2,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,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 = X2
| X0 = X2
| X0 = X1 ),
inference(component_clause,[status(thm)],[f3104]) ).
fof(f3107,plain,
( ~ sQ17_spl
| ~ sQ7_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f3102,f3104,f1779,f2374]) ).
fof(f3108,definition,
! [X0,X1,X2] :
( sQ53_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____,X2,v_a_H____,X1,v_b_H____,X0)),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),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(v_P_H____,X2,v_a_H____,X1,v_b_H____,X0)),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
| X0 = X1
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f3109,plain,
! [X0,X1,X2] :
( ~ sQ53_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____,X2,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| 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)))
| v_b_H____ = X0
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_H____,X2,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(component_clause,[status(thm)],[f3108]) ).
fof(f3111,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ7_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f3101,f3108,f1779,f1776,f1721]) ).
fof(f3112,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ52_spl
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X4,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_a_H____
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P_H____,X0,X4,X1,X3,X2)),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_H____,v_P_H____,X4,v_a_H____,X3,v_b_H____)),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),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X0,X4,X1,X3,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| X4 = v_b_H____
| X3 = X1
| X1 = X2
| ~ 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(duplicate_literals_removal,[status(thm)],[f3105]) ).
fof(f3136,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ26_spl
| X2 = X1
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X1,X5,X2,X4)),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)))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X1,X5,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,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 = X5
| X4 = X5
| X4 = X1
| v_b_H____ = X3
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X0
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| ~ 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_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f2642,f1679]) ).
fof(f3140,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ54_spl
<=> ( X2 = X1
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X1,X5,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X1,X5,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,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 = X5
| X4 = X5
| X4 = X1
| v_b_H____ = X3
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X0
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| ~ 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_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f3141,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ54_spl
| X2 = X1
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X1,X5,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X1,X5,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,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 = X5
| X4 = X5
| X4 = X1
| v_b_H____ = X3
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X0
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X3,X2,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| ~ 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_H____,X3,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X0 = v_a_H____ ),
inference(component_clause,[status(thm)],[f3140]) ).
fof(f3143,plain,
( ~ sQ26_spl
| ~ sQ7_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f3136,f3140,f1779,f2613]) ).
fof(f3147,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ54_spl
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X1,X4,X0,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,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_a_H____ = X3
| X0 = X4
| X1 = X5
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X1,X4,X0,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X3 = X2
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X2,X0,X3)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,X2,X0,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ 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_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = v_b_H____
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f3141]) ).
fof(f3154,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ26_spl
| ~ sQ27_spl
| X1 = X0
| v_b_H____ = X0
| v_a_H____ = X1
| X1 = X2
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X0,X3,X1)),X4)
| X3 = X0
| X1 = X2
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X0,X3,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 = X0
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| X3 = X0
| X2 = X3
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0 ),
inference(resolution,[status(thm)],[f2626,f2723]) ).
fof(f3155,definition,
! [X0,X1,X2,X3,X4] :
( sQ55_spl
<=> ( X1 = X0
| v_b_H____ = X0
| v_a_H____ = X1
| X1 = X2
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X0,X3,X1)),X4)
| X3 = X0
| X1 = X2
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X2,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| X3 = X0
| X2 = X3
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f3158,plain,
( ~ sQ26_spl
| ~ sQ27_spl
| ~ sQ4_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f3154,f3155,f1768,f2617,f2613]) ).
fof(f3173,plain,
! [X0,X1] :
( ~ sQ53_spl
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),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),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3109,f1672]) ).
fof(f3174,plain,
! [X0,X1] :
( ~ sQ53_spl
| v_a_H____ = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b_H____
| X0 = X1
| ~ c_in(c_Pair(X0,X1,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____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3109,f1673]) ).
fof(f3178,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ33_spl
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ),
inference(resolution,[status(thm)],[f2694,f1672]) ).
fof(f3179,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ33_spl
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X2,X4,X3)),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,X0,X5,X1,X4)),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(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X0,X5,X1,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X3
| X1 = X5
| ~ 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_H____,X2,v_a_H____,X3,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X3 = v_a_H____
| X0 = X4
| v_b_H____ = X2
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X2,X4,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X2 = X3
| X0 = X1 ),
inference(resolution,[status(thm)],[f2694,f1673]) ).
fof(f3183,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ37_spl
| X0 = v_a____
| 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____,X1,v_b____,X0)),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)))
| X0 = X1
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____
| v_b____ = X1
| v_a____ = v_b____
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| X1 = v_b____
| ~ 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____,X1,v_b____,X0)),X2)
| X0 = v_a_H____
| X1 = v_b_H____
| v_a____ = X0 ),
inference(resolution,[status(thm)],[f2729,f2626]) ).
fof(f3184,plain,
! [X0,X1,X2,X3] :
( ~ sQ37_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____,X1,v_b____,X0)),X3)
| X0 = X1
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),X2)
| ~ 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_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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| v_a_H____ = X0
| X1 = v_b____
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f2729,f1923]) ).
fof(f3186,definition,
! [X0,X1,X2] :
( sQ56_spl
<=> ( X0 = v_a____
| 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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ 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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____
| v_b____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X1
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| X1 = v_b____
| ~ 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____,X1,v_b____,X0)),X2)
| X0 = v_a_H____
| X1 = v_b_H____
| v_a____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f3189,plain,
( ~ sQ27_spl
| ~ sQ37_spl
| ~ sQ4_spl
| sQ1_spl
| sQ3_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f3183,f3186,f1765,f1724,f1768,f2728,f2617]) ).
fof(f3198,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ37_spl
| ~ sQ35_spl
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,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_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X2 = v_b____
| ~ 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____,X2,v_b____,X3)),X4)
| X3 = v_a_H____
| X2 = v_b_H____
| v_a____ = X3
| X0 = X1
| X3 = X2
| X3 = v_a____
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X3,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____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X2
| X1 = X2
| X1 = 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(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2692,f2729]) ).
fof(f3199,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ26_spl
| ~ sQ35_spl
| X4 = X2
| v_b_H____ = X2
| v_a_H____ = X4
| X4 = X5
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X4,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_H____,v_P_H____,X2,v_a_H____,X4,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X3
| ~ c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X5,X2,X3,X4)),X6)
| X3 = X2
| X0 = X1
| X4 = X2
| X4 = X5
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X5,X2,X3,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X5
| c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = X2
| X1 = 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(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2692,f2723]) ).
fof(f3200,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ58_spl
<=> ( X4 = X2
| v_b_H____ = X2
| v_a_H____ = X4
| X4 = X5
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X4,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_H____,v_P_H____,X2,v_a_H____,X4,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X3
| ~ c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X5,X2,X3,X4)),X6)
| X3 = X2
| X0 = X1
| X4 = X2
| X4 = X5
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P_H____,X5,X2,X3,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X5
| c_in(c_Pair(X5,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = X2
| X1 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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,[sQ58_spl])],[split_symbol_definition]) ).
fof(f3203,plain,
( ~ sQ26_spl
| ~ sQ35_spl
| ~ sQ4_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f3199,f3200,f1768,f2688,f2613]) ).
fof(f3204,definition,
! [X0,X1,X2,X3,X4] :
( sQ59_spl
<=> ( ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,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_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X2 = v_b____
| ~ 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____,X2,v_b____,X3)),X4)
| X3 = v_a_H____
| X2 = v_b_H____
| v_a____ = X3
| X0 = X1
| X3 = X2
| X3 = v_a____
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X3,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____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,X2,v_b____,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X2
| X1 = X2
| X1 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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,[sQ59_spl])],[split_symbol_definition]) ).
fof(f3207,plain,
( ~ sQ37_spl
| ~ sQ35_spl
| sQ3_spl
| sQ1_spl
| ~ sQ4_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f3198,f3204,f1768,f1724,f1765,f2688,f2728]) ).
fof(f3238,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| X1 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X0,X3,X1,X2)),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)))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X0,X3,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,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 = X3
| X2 = X3
| X2 = X0
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3173,f1679]) ).
fof(f3239,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| X1 = X0
| X1 = X4
| X3 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X4,X0,X3,X1)),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)))
| c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X4,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ 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)))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3173,f1677]) ).
fof(f3240,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(X4,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(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| X1 = X0
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| ~ 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)))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3173,f1681]) ).
fof(f3241,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| X0 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X0,X2,X1,X3)),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)))
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X0,X2,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X4,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 = X2
| X0 = X1
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3173,f1683]) ).
fof(f3242,definition,
! [X0,X1,X2,X3,X4] :
( sQ60_spl
<=> ( X0 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X0,X2,X1,X3)),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X0,X2,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X4,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 = X2
| X0 = X1
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f3245,plain,
( ~ sQ53_spl
| ~ sQ7_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f3241,f3242,f1779,f3108]) ).
fof(f3246,definition,
! [X0,X1,X2,X3,X4] :
( sQ61_spl
<=> ( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(X4,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(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| X1 = X0
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f3247,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ61_spl
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| ~ c_in(X4,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(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| X1 = X0
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f3246]) ).
fof(f3249,plain,
( ~ sQ53_spl
| ~ sQ7_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f3240,f3246,f1779,f3108]) ).
fof(f3250,definition,
! [X0,X1,X2,X3,X4] :
( sQ62_spl
<=> ( X1 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X4,X0,X3,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(v_P_H____,X4,X0,X3,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,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 = X3
| X2 = X3
| X2 = X0
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f3253,plain,
( ~ sQ53_spl
| ~ sQ7_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f3238,f3250,f1779,f3108]) ).
fof(f3254,definition,
! [X0,X1,X2,X3,X4] :
( sQ63_spl
<=> ( X1 = X0
| X1 = X4
| X3 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X4,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X4,X0,X3,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ 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)))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f3257,plain,
( ~ sQ53_spl
| ~ sQ7_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f3239,f3254,f1779,f3108]) ).
fof(f3258,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ61_spl
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,v_P_H____,X3,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ 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)))
| X0 = X4
| X4 = X3
| X3 = X1
| ~ 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_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X2,v_P_H____,X3,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literals_removal,[status(thm)],[f3247]) ).
fof(f3262,plain,
( ~ sQ17_spl
| ~ sQ31_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a_H____
| v_b____ = v_a____
| 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_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(resolution,[status(thm)],[f2656,f2633]) ).
fof(f3263,plain,
( ~ sQ17_spl
| ~ sQ31_spl
| sQ1_spl
| sQ14_spl
| sQ3_spl
| sQ13_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f3262,f2634,f2357,f1765,f2360,f1724,f2655,f2374]) ).
fof(f3270,plain,
! [X0,X1,X2,X3] :
( ~ sQ26_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____,X1,v_b____,X0)),X3)
| X0 = X1
| X0 = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_b____
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| X1 = 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_H____,X1,v_a_H____,X0,v_b_H____)),X2)
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f3042,f1927]) ).
fof(f3276,definition,
! [X0,X1,X2,X3] :
( sQ65_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____,X1,v_b____,X0)),X3)
| X0 = X1
| X0 = v_a____
| X1 = v_b____
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = 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_H____,X1,v_a_H____,X0,v_b_H____)),X2)
| ~ c_in(c_Pair(X1,X0,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____,X1,v_b____,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f3277,plain,
! [X0,X1,X2,X3] :
( ~ sQ65_spl
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| ~ c_in(c_Pair(X0,X1,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____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ),
inference(component_clause,[status(thm)],[f3276]) ).
fof(f3279,plain,
( ~ sQ26_spl
| sQ1_spl
| sQ3_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f3270,f3276,f1765,f1724,f2613]) ).
fof(f3316,plain,
! [X0] :
( ~ sQ53_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____)),X0)
| v_a_H____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_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))
| v_a____ = v_b_H____
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f3174,f1927]) ).
fof(f3318,plain,
( ~ sQ53_spl
| sQ42_spl
| sQ14_spl
| sQ1_spl
| ~ sQ25_spl
| sQ13_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f3316,f1765,f2357,f2566,f1724,f2360,f2796,f3108]) ).
fof(f3320,plain,
! [X0,X1,X2,X3] :
( ~ sQ26_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____,X0,v_b____,X1)),X3)
| X1 = v_a_H____
| X0 = v_b_H____
| v_b____ = v_a____
| ~ 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_H____,X0,v_a_H____,X1,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| v_a____ = X1
| X1 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3063,f1927]) ).
fof(f3323,definition,
! [X0,X1,X2,X3] :
( sQ66_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____,X0,v_b____,X1)),X3)
| X1 = v_a_H____
| 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_P_H____,v_sko__CHAINED__1(v_P_H____,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(c_Pair(X0,X1,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____,X0,v_b____,X1)),X2)
| v_a____ = X1
| X1 = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f3326,plain,
( ~ sQ26_spl
| sQ3_spl
| sQ66_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f3320,f1724,f3323,f1765,f2613]) ).
fof(f3342,plain,
! [X0,X1,X2,X3] :
( ~ sQ52_spl
| X0 = X2
| X2 = X3
| ~ c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| v_b_H____ = X3
| X1 = v_a_H____
| c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(resolution,[status(thm)],[f3112,f1672]) ).
fof(f3343,plain,
! [X0,X1,X2,X3] :
( ~ sQ52_spl
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X3,X1,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X2 = X1
| X3 = v_b_H____
| X1 = X0
| X3 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X0,v_b_H____)),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(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,X3,X1,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X0,v_b_H____)),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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f3112,f1673]) ).
fof(f3345,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ54_spl
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f3147,f1672]) ).
fof(f3346,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ54_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_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X4,X0,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X0,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P_H____,v_P____,X4,X0,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X3
| X1 = X2
| X2 = X3
| c_in(c_Pair(X0,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X2 = v_b_H____
| X5 = X0
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X3,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X4,X2,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_a_H____
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X4,X2,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(resolution,[status(thm)],[f3147,f1673]) ).
fof(f3349,plain,
! [X0] :
( sQ29_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____)),X0) ),
inference(resolution,[status(thm)],[f2636,f1925]) ).
fof(f3352,plain,
! [X0] :
( sQ29_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____)),X0) ),
inference(resolution,[status(thm)],[f2636,f1923]) ).
fof(f3354,plain,
( sQ29_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f3352,f2637,f2634]) ).
fof(f3446,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ33_spl
| X4 = X5
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X5,X7,X4,X6)),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)))
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X5,X7,X4,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,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)))
| X4 = X7
| X6 = X7
| X6 = X5
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ),
inference(resolution,[status(thm)],[f3178,f1679]) ).
fof(f3447,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ33_spl
| X4 = X5
| X4 = X8
| X7 = X5
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X8,X5,X7,X4)),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)))
| c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X8,X5,X7,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X7 = X8
| ~ c_in(X6,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)))
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ),
inference(resolution,[status(thm)],[f3178,f1677]) ).
fof(f3448,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ33_spl
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X8,v_P_H____,X7,X5,X6,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X5
| ~ c_in(X8,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(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X7
| X4 = X5
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(X8,v_P_H____,X7,X5,X6,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X7
| ~ 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)))
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ),
inference(resolution,[status(thm)],[f3178,f1681]) ).
fof(f3449,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ33_spl
| X5 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X5,X6,X4,X7)),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)))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X5,X6,X4,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X6
| ~ c_in(X8,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)))
| X7 = X6
| X5 = X4
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ),
inference(resolution,[status(thm)],[f3178,f1683]) ).
fof(f3450,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ67_spl
<=> ( X5 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X5,X6,X4,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X5,X6,X4,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X6
| ~ c_in(X8,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)))
| X7 = X6
| X5 = X4
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f3453,plain,
( ~ sQ33_spl
| ~ sQ7_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f3449,f3450,f1779,f2680]) ).
fof(f3454,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ68_spl
<=> ( c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X8,v_P_H____,X7,X5,X6,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X5
| ~ c_in(X8,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(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X7
| X4 = X5
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(X8,v_P_H____,X7,X5,X6,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X7
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f3457,plain,
( ~ sQ33_spl
| ~ sQ7_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f3448,f3454,f1779,f2680]) ).
fof(f3458,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ69_spl
<=> ( X4 = X5
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X5,X7,X4,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X5,X7,X4,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,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)))
| X4 = X7
| X6 = X7
| X6 = X5
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f3461,plain,
( ~ sQ33_spl
| ~ sQ7_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f3446,f3458,f1779,f2680]) ).
fof(f3462,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ70_spl
<=> ( X4 = X5
| X4 = X8
| X7 = X5
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X8,X5,X7,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X8,X5,X7,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X7 = X8
| ~ c_in(X6,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)))
| X0 = X2
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b_H____
| X2 = v_a_H____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X3,X1,X2)),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_H____,v_P_H____,X3,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X5,X0,X4,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X5 = X1
| X0 = X4
| X2 = X3
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f3465,plain,
( ~ sQ33_spl
| ~ sQ7_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f3447,f3462,f1779,f2680]) ).
fof(f3484,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ33_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____,X3,v_b____,X2)),X4)
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,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____,X3,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| v_b____ = X3
| ~ 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_H____,X0,v_a_H____,X1,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = v_a_H____
| v_a____ = X2
| v_b_H____ = X0
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| X0 = X1
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f3179,f1927]) ).
fof(f3486,definition,
! [X0,X1,X2,X3,X4] :
( sQ71_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____,X3,v_b____,X2)),X4)
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,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____,X3,v_b____,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| v_b____ = X3
| ~ 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_H____,X0,v_a_H____,X1,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = v_a_H____
| v_a____ = X2
| v_b_H____ = X0
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X0,X2,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X0
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f3489,plain,
( ~ sQ33_spl
| sQ1_spl
| sQ71_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f3484,f1765,f3486,f1724,f2680]) ).
fof(f3505,plain,
! [X0] :
( ~ sQ37_spl
| ~ sQ61_spl
| v_b_H____ = v_a_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____,v_P_H____,v_a____,v_a_H____,v_b____,v_b_H____)),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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,v_a_H____,v_b_H____,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_H____,v_P_H____,v_a_H____,v_a_H____,v_b_H____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = v_a_H____
| v_a_H____ = v_b_H____
| v_a_H____ = v_b____
| v_b_H____ = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = v_a_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_H____,v_a_H____,v_a_H____,v_b_H____,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_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_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_a_H____ = v_b____
| v_b____ = v_a____
| 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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,v_a_H____,v_b_H____,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = v_b_H____ ),
inference(resolution,[status(thm)],[f3258,f3184]) ).
fof(f3508,plain,
( ~ sQ37_spl
| ~ sQ61_spl
| sQ30_spl
| sQ1_spl
| sQ31_spl
| ~ sQ4_spl
| sQ14_spl
| sQ3_spl
| sQ13_spl
| ~ sQ32_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f3505,f1776,f2658,f2357,f1765,f2360,f1768,f2655,f1724,f2637,f3246,f2728]) ).
fof(f3533,plain,
! [X0,X1,X2,X3] :
( ~ sQ61_spl
| ~ sQ65_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_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____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| ~ 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)))
| X0 = v_b____
| v_b____ = v_a____
| v_a____ = X1
| ~ 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_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f3277,f3258]) ).
fof(f3534,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ35_spl
| ~ sQ65_spl
| X4 = X5
| X1 = X0
| X1 = v_a____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X4,X1,X5)),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____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X4
| ~ 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_H____,X4,v_a_H____,X5,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X4,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X0
| X5 = X0
| X5 = 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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X4,v_a_H____,X5,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f3277,f2692]) ).
fof(f3535,plain,
! [X0,X1,X2,X3] :
( ~ sQ27_spl
| ~ sQ65_spl
| X1 = v_a____
| 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____,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 = X0
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b____ = X0
| v_a____ = v_b____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f3277,f2626]) ).
fof(f3538,definition,
! [X0,X1,X2,X3] :
( sQ72_spl
<=> ( X1 = v_a____
| 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____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = v_a_H____
| v_b____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f3541,plain,
( ~ sQ27_spl
| ~ sQ65_spl
| ~ sQ4_spl
| sQ1_spl
| sQ3_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f3535,f3538,f1765,f1724,f1768,f3276,f2617]) ).
fof(f3543,definition,
! [X0,X1,X2,X3] :
( sQ73_spl
<=> ( v_b_H____ = X0
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,v_a_H____,X0,v_b_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____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| X0 = v_b____
| v_a____ = X1
| ~ 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_H____,v_a_H____,X0,v_b_H____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f3546,plain,
( ~ sQ61_spl
| ~ sQ65_spl
| sQ1_spl
| ~ sQ4_spl
| sQ3_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f3533,f3543,f1765,f1768,f1724,f3276,f3246]) ).
fof(f3547,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ74_spl
<=> ( X4 = X5
| X1 = X0
| X1 = v_a____
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X4,X1,X5)),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____,X0,v_b____,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b_H____ = X4
| ~ 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_H____,X4,v_a_H____,X5,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X0,X4,X1,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X0
| X5 = X0
| X5 = v_a_H____
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X4,v_a_H____,X5,v_b_H____)),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(v_P_H____,v_sko__CHAINED__1(v_P_H____,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(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_H____,X0,v_a_H____,X1,v_b_H____)),X3)
| X1 = v_a_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____,v_P_H____,v_a____,X0,v_b____,X1)),X2)
| X0 = v_b_H____
| X0 = X1
| v_a____ = X1
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f3550,plain,
( ~ sQ35_spl
| ~ sQ65_spl
| sQ3_spl
| sQ1_spl
| ~ sQ4_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f3534,f3547,f1768,f1724,f1765,f3276,f2688]) ).
fof(f3555,plain,
( ~ sQ5_spl
| sQ25_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))
| v_b____ = v_a____
| 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),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_b_H____ ),
inference(resolution,[status(thm)],[f2568,f1774]) ).
fof(f3562,plain,
( ~ sQ5_spl
| sQ25_spl
| sQ15_spl
| sQ3_spl
| sQ14_spl
| ~ sQ4_spl
| sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f3555,f2357,f1724,f1768,f2360,f1765,f2363,f2566,f1773]) ).
fof(f3595,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ52_spl
| X3 = X0
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X0,X5,X3,X4)),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)))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X0,X5,X3,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,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 = X5
| X4 = X5
| X4 = X0
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f3342,f1679]) ).
fof(f3596,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ52_spl
| X3 = X0
| X3 = X6
| X5 = X0
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X6,X0,X5,X3)),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)))
| c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X6,X0,X5,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X4,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)))
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f3342,f1677]) ).
fof(f3597,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ52_spl
| c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X5,X0,X4,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X0
| ~ c_in(X6,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(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X5
| X3 = X0
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X5,X0,X4,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| ~ 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)))
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f3342,f1681]) ).
fof(f3598,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ52_spl
| X0 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X0,X4,X3,X5)),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)))
| c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X0,X4,X3,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ c_in(X6,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)))
| X5 = X4
| X0 = X3
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ),
inference(resolution,[status(thm)],[f3342,f1683]) ).
fof(f3599,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ75_spl
<=> ( X0 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X0,X4,X3,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X0,X4,X3,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X4
| ~ c_in(X6,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)))
| X5 = X4
| X0 = X3
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f3602,plain,
( ~ sQ52_spl
| ~ sQ7_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f3598,f3599,f1779,f3104]) ).
fof(f3603,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ76_spl
<=> ( X3 = X0
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X6,X0,X5,X3,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(v_P_H____,X6,X0,X5,X3,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,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 = X5
| X4 = X5
| X4 = X0
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f3606,plain,
( ~ sQ52_spl
| ~ sQ7_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f3595,f3603,f1779,f3104]) ).
fof(f3607,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ77_spl
<=> ( c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X5,X0,X4,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X0
| ~ c_in(X6,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(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X5
| X3 = X0
| c_in(c_Pair(X5,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X5,X0,X4,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f3610,plain,
( ~ sQ52_spl
| ~ sQ7_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f3597,f3607,f1779,f3104]) ).
fof(f3611,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ78_spl
<=> ( X3 = X0
| X3 = X6
| X5 = X0
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X4,v_P_H____,X6,X0,X5,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__CHAINED__1(X4,v_P_H____,X6,X0,X5,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X4,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)))
| X0 = X3
| X3 = X2
| ~ c_in(c_Pair(X0,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X0,X1,X3)),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_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,v_a_H____,X1,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| v_b_H____ = X2
| X1 = v_a_H____
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f3614,plain,
( ~ sQ52_spl
| ~ sQ7_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f3596,f3611,f1779,f3104]) ).
fof(f3670,plain,
! [X0,X1,X2] :
( ~ sQ52_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____,X1,v_a____,X0,v_b____)),X2)
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X1,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X1
| v_b____ = v_a____
| X1 = v_b_H____
| v_a____ = X0
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,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_P_H____,v_sko__CHAINED__1(v_P_H____,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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ),
inference(resolution,[status(thm)],[f3343,f1927]) ).
fof(f3673,definition,
! [X0,X1,X2] :
( sQ79_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____,X1,v_a____,X0,v_b____)),X2)
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X1,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = X1
| X1 = v_b_H____
| v_a____ = X0
| X1 = 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____,v_sko__CHAINED__1(v_P_H____,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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X0,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a_H____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f3676,plain,
( ~ sQ52_spl
| sQ3_spl
| sQ1_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f3670,f3673,f1724,f1765,f3104]) ).
fof(f3733,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ54_spl
| X5 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X4,X7,X5,X6)),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)))
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X4,X7,X5,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,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)))
| X5 = X7
| X6 = X7
| X6 = X4
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f3345,f1679]) ).
fof(f3734,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ54_spl
| X5 = X4
| X5 = X8
| X7 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X8,X4,X7,X5)),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)))
| c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X8,X4,X7,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X7 = X8
| ~ c_in(X6,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)))
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f3345,f1677]) ).
fof(f3735,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ54_spl
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X8,v_P_H____,X7,X4,X6,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X4
| ~ c_in(X8,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(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X7
| X5 = X4
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(X8,v_P_H____,X7,X4,X6,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X7
| ~ 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)))
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f3345,f1681]) ).
fof(f3736,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ54_spl
| X4 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X4,X6,X5,X7)),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)))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X4,X6,X5,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X8,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)))
| X7 = X6
| X4 = X5
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ),
inference(resolution,[status(thm)],[f3345,f1683]) ).
fof(f3737,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ80_spl
<=> ( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X8,v_P_H____,X7,X4,X6,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X4
| ~ c_in(X8,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(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X7
| X5 = X4
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(X8,v_P_H____,X7,X4,X6,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X6 = X7
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f3740,plain,
( ~ sQ54_spl
| ~ sQ7_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f3735,f3737,f1779,f3140]) ).
fof(f3741,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ81_spl
<=> ( X4 = X7
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X4,X6,X5,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X4,X6,X5,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X6
| ~ c_in(X8,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)))
| X7 = X6
| X4 = X5
| c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f3744,plain,
( ~ sQ54_spl
| ~ sQ7_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f3736,f3741,f1779,f3140]) ).
fof(f3745,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ82_spl
<=> ( X5 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,X8,X4,X7,X5,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__CHAINED__1(v_P_H____,X8,X4,X7,X5,X6)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,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)))
| X5 = X7
| X6 = X7
| X6 = X4
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f3748,plain,
( ~ sQ54_spl
| ~ sQ7_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f3733,f3745,f1779,f3140]) ).
fof(f3749,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ83_spl
<=> ( X5 = X4
| X5 = X8
| X7 = X4
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X6,v_P_H____,X8,X4,X7,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__CHAINED__1(X6,v_P_H____,X8,X4,X7,X5)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X7 = X8
| ~ c_in(X6,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)))
| X0 = X2
| ~ 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_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(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X4
| X2 = X3
| X1 = v_b_H____
| X3 = X4
| X0 = X1
| X5 = X2
| X1 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,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(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X4,X3,X5)),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_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X2,X1,X3,X0)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a_H____ ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f3752,plain,
( ~ sQ54_spl
| ~ sQ7_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f3734,f3749,f1779,f3140]) ).
fof(f3758,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ54_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____,X3,v_a____,X0,v_b____)),X4)
| ~ 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_H____,X1,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X3,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X0 = X1
| X1 = X2
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X0
| X1 = v_b_H____
| v_b____ = v_a____
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b____
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X1,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = v_a_H____
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X1,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0 ),
inference(resolution,[status(thm)],[f3346,f1927]) ).
fof(f3760,definition,
! [X0,X1,X2,X3,X4] :
( sQ84_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____,X3,v_a____,X0,v_b____)),X4)
| ~ 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_H____,X1,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,X3,v_a____,X0,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X0 = X1
| X1 = X2
| X3 = X0
| X1 = v_b_H____
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X1,v_a_H____,X2,v_b_H____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = v_b____
| ~ c_in(c_Pair(X3,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X1,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = v_a_H____
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P_H____,X3,X1,X0,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f3763,plain,
( ~ sQ54_spl
| sQ1_spl
| sQ3_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f3758,f3760,f1765,f1724,f3140]) ).
fof(f3777,plain,
( ~ sQ31_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2656,f3349]) ).
fof(f3778,plain,
( ~ sQ31_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f3777]) ).
fof(f3779,plain,
$false,
inference(sat_refutation,[status(thm)],[f1727,f1728,f1782,f1784,f1786,f2036,f2043,f2045,f2047,f2351,f2377,f2394,f2404,f2569,f2571,f2573,f2616,f2620,f2624,f2640,f2661,f2663,f2683,f2687,f2691,f2727,f2731,f2799,f2828,f3033,f3067,f3072,f3107,f3111,f3143,f3158,f3189,f3203,f3207,f3245,f3249,f3253,f3257,f3263,f3279,f3318,f3326,f3354,f3453,f3457,f3461,f3465,f3489,f3508,f3541,f3546,f3550,f3562,f3602,f3606,f3610,f3614,f3676,f3740,f3744,f3748,f3752,f3763,f3778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT066-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/10.46 % Computer : n005.cluster.edu
% 0.18/10.46 % Model : x86_64 x86_64
% 0.18/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.46 % Memory : 8046.5625MB
% 0.18/10.46 % OS : Linux 6.8.0-71-generic
% 0.18/10.47 % CPULimit : 300
% 0.18/10.47 % WCLimit : 300
% 0.18/10.47 % DateTime : Mon Sep 21 04:28:59 UTC 2026
% 0.18/10.47 % CPUTime :
% 0.24/10.55 % Drodi V4.1.1
% 134.76/27.68 % Refutation found
% 134.76/27.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 134.76/27.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 127.47/29.04 % Elapsed time: 18.346386 seconds
% 127.47/29.04 % CPU time: 127.604611 seconds
% 127.47/29.04 % Total memory used: 820.412 MB
% 127.47/29.04 % Net memory used: 774.914 MB
%------------------------------------------------------------------------------