%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT069-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 227.07s 29.23s
% Output : CNFRefutation 71.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 229
% Syntax : Number of formulae : 768 ( 81 unt; 161 def)
% Number of atoms : 2160 ( 239 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 2434 (1042 ~;1231 |; 0 &)
% ( 161 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 178 ( 176 usr; 162 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 10 con; 0-5 aty)
% Number of variables : 755 ( 755 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [T_a,V_x] :
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [V_B,V_A,T_a] : c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [T_a,V_x,V_y] :
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [V_a,V_A,T_a] : c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [V_x,V_B,T_a,V_A] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [V_y,V_A,T_a,V_x] :
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [V_a,V_A,T_a] : c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,axiom,
! [V_B,V_x,V_A,T_a] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(V_B,V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [V_A,V_B,T_a,V_x] :
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [T_a,V_x] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,axiom,
! [V_c,T_a,T_b,V_A] :
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [T_a,V_x,V_y] :
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,axiom,
! [T_a,V_x,V_y] :
( V_x = V_y
| c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f167,axiom,
! [T_a,V_A,V_B] :
( V_B = c_Orderings_Obot__class_Obot(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f184,axiom,
! [T_a,V_x,V_y] :
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f216,axiom,
! [T_a,V_x] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f287,axiom,
! [V_x,V_A,T_a] : hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f296,axiom,
! [V_a,V_A,T_a] :
( ~ c_in(V_a,V_A,T_a)
| c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f355,axiom,
! [V_A,T_a,V_B] : c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f499,axiom,
! [V_A,T_a] : c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f502,axiom,
! [V_A,T_a] : c_Relation_Oantisym(c_Relation_OId__on(V_A,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f517,axiom,
! [V_A,T_a] : c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f539,axiom,
! [V_r,T_a,T_b] : c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f581,axiom,
! [V_a,V_c,T_a,V_r,V_b] :
( ~ c_Relation_Otrans(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f582,axiom,
! [V_a,V_b,T_a,T_b,V_r] :
( ~ c_in(c_Pair(V_b,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(c_Pair(V_a,V_b,T_a,T_b),c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f585,axiom,
! [V_x,T_a,V_r] :
( ~ c_Relation_Oirrefl(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f592,axiom,
! [V_a,T_a,V_r] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f594,axiom,
! [V_x,V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f595,axiom,
! [V_x,V_y,T_a,V_r] :
( ~ c_Relation_Oantisym(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_x = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f602,axiom,
! [V_a,T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f605,axiom,
! [V_y,V_x,T_a,V_r] :
( ~ c_Relation_Osym(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f607,axiom,
! [V_a,V_c,T_a,T_c,V_r,V_s,T_b,V_b] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| ~ c_in(c_Pair(V_b,V_c,T_b,T_c),V_s,tc_prod(T_b,T_c))
| c_in(c_Pair(V_a,V_c,T_a,T_c),c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),tc_prod(T_a,T_c)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f612,axiom,
! [V_x,V_y,V_L,V_z] :
( V_x = V_z
| V_x = V_y
| ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f617,axiom,
! [V_x,V_y,V_L] :
( c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_y = V_x
| V_x = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f622,axiom,
! [V_xa,V_x,V_L] :
( c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_xa = V_x
| V_xa = V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f624,axiom,
! [V_a,V_b] :
( V_a = V_b
| c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f627,axiom,
! [V_a,V_r,T_a,V_b] :
( ~ c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f629,axiom,
! [V_b,V_r,V_A,T_a,T_b,V_a] :
( ~ c_in(V_a,V_A,T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_b,c_Relation_OImage(V_r,V_A,T_a,T_b),T_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f632,axiom,
! [V_x,T_a,V_A] :
( ~ c_in(V_x,V_A,T_a)
| c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId__on(V_A,T_a),tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f633,axiom,
! [V_y,V_A,T_a,V_x,V_r] :
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f635,axiom,
! [V_a,V_r,T_b,T_a,V_x] :
( ~ c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f638,axiom,
! [V_a,V_r,T_a,T_b,V_b] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f643,axiom,
! [V_y,V_A,T_a,V_x,V_r] :
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f651,axiom,
! [V_i] :
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f652,axiom,
( v_a____ = v_b_H____
| v_b____ = v_a_H____
| ~ 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/sandbox/benchmark/theBenchmark.p') ).
fof(f653,axiom,
( v_a____ = v_b_H____
| v_b____ = v_a_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))
| 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/sandbox/benchmark/theBenchmark.p') ).
fof(f654,axiom,
! [V_x,V_S,T_a] :
( ~ hBOOL(hAPP(V_S,V_x))
| c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f655,axiom,
! [V_S,V_x,T_a] :
( ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f656,axiom,
( ~ 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))
| v_a____ = v_b_H____
| v_b____ != v_a_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f657,axiom,
( ~ 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))
| v_a____ = v_b_H____
| v_b____ != v_a_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f658,axiom,
( v_b____ = v_a_H____
| ~ 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))
| v_a____ != v_b_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f659,axiom,
( v_b____ = v_a_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))
| 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____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f661,axiom,
! [V_i] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,V_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f662,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f663,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f665,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f666,axiom,
! [V_a,V_b,V_P,V_P_H] :
( V_a = V_b
| ~ 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_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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/sandbox/benchmark/theBenchmark.p') ).
fof(f667,axiom,
! [V_b,V_a,V_P_H,V_P] :
( V_a = V_b
| ~ 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_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_b)),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_b,V_a,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/sandbox/benchmark/theBenchmark.p') ).
fof(f668,axiom,
! [V_a,V_b,V_P,V_P_H] :
( V_a = V_b
| ~ 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_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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/sandbox/benchmark/theBenchmark.p') ).
fof(f672,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/sandbox/benchmark/theBenchmark.p') ).
fof(f673,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/sandbox/benchmark/theBenchmark.p') ).
fof(f678,axiom,
! [T_2,T_1] :
( ~ class_Lattices_Oboolean__algebra(T_1)
| class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f684,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f685,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f687,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f688,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f690,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f702,plain,
! [T_a] :
( ! [V_x] : c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f703,plain,
! [X0,X1] :
( X1 = c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ),
inference(cnf_transformation,[status(thm)],[f702]) ).
fof(f716,plain,
! [X0,X1,X2] : c_Set_Oimage(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f738,plain,
! [X0,X1,X2] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f757,plain,
! [T_a] :
( ! [V_x,V_y] : c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f758,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f757]) ).
fof(f766,plain,
! [X0,X1,X2] : c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = c_Set_Oinsert(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f772,plain,
! [V_x,V_B,T_a] :
( ! [V_A] : ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f773,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(c_Set_Oinsert(X0,X1,X2),X3,tc_fun(X2,tc_bool)) ),
inference(cnf_transformation,[status(thm)],[f772]) ).
fof(f775,plain,
! [V_A,V_x] :
( ~ hBOOL(hAPP(V_A,V_x))
| ! [V_y,T_a] : hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f776,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f775]) ).
fof(f827,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X2,X0),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f854,plain,
! [V_B,V_x,V_A] :
( ! [T_a] : ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(V_B,V_x)) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f855,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X3,tc_bool)),X1))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f854]) ).
fof(f858,plain,
! [V_A,V_x] :
( ~ hBOOL(hAPP(V_A,V_x))
| ! [V_B,T_a] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f859,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X3,tc_bool)),X1))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f858]) ).
fof(f882,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f885,plain,
! [T_b,V_A] :
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ! [V_c,T_a] : c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f886,plain,
! [X0,X1,X2,X3] :
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Set_Oimage(c_COMBK(X0,X1,X2),X3,X2,X1) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
inference(cnf_transformation,[status(thm)],[f885]) ).
fof(f896,plain,
! [T_a] :
( ! [V_x,V_y] : c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f897,plain,
! [X0,X1,X2] :
( X1 = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[status(thm)],[f896]) ).
fof(f900,plain,
! [V_x,V_y] :
( V_x = V_y
| ! [T_a] :
( c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
| ~ class_Lattices_Oboolean__algebra(T_a) ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f901,plain,
! [X0,X1,X2] :
( c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0)
| X1 = X2
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[status(thm)],[f900]) ).
fof(f937,plain,
! [T_a,V_B] :
( V_B = c_Orderings_Obot__class_Obot(T_a)
| ! [V_A] : c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
inference(miniscoping,[status(thm)],[f167]) ).
fof(f938,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = X1
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2) != c_Orderings_Obot__class_Obot(X2) ),
inference(cnf_transformation,[status(thm)],[f937]) ).
fof(f965,plain,
! [T_a] :
( ! [V_x,V_y] : c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f966,plain,
! [X0,X1,X2] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[status(thm)],[f965]) ).
fof(f1010,plain,
! [T_a] :
( ! [V_x] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(miniscoping,[status(thm)],[f216]) ).
fof(f1011,plain,
! [X0,X1] :
( X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[status(thm)],[f1010]) ).
fof(f1124,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f1138,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| c_Set_Oinsert(X0,c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) = X1 ),
inference(cnf_transformation,[status(thm)],[f296]) ).
fof(f1230,plain,
! [X0,X1,X2] : c_Relation_OImage(c_Relation_OId__on(X0,X1),X2,X1,X1) = c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_fun(X1,tc_bool)),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f1434,plain,
! [X0,X1] : c_Relation_Otrans(c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f499]) ).
fof(f1437,plain,
! [X0,X1] : c_Relation_Oantisym(c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f502]) ).
fof(f1452,plain,
! [X0,X1] : c_Relation_Osym(c_Relation_OId__on(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f517]) ).
fof(f1479,plain,
! [X0,X1,X2] : X0 = c_Relation_Oconverse(c_Relation_Oconverse(X0,X1,X2),X2,X1),
inference(cnf_transformation,[status(thm)],[f539]) ).
fof(f1541,plain,
! [T_a,V_r] :
( ~ c_Relation_Otrans(V_r,T_a)
| ! [V_a,V_b] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ! [V_c] :
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ) ),
inference(miniscoping,[status(thm)],[f581]) ).
fof(f1542,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X3,X2)
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f1541]) ).
fof(f1543,plain,
! [X0,X1,X2,X3,X4] :
( c_in(c_Pair(X1,X0,X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2))
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f582]) ).
fof(f1546,plain,
! [T_a,V_r] :
( ~ c_Relation_Oirrefl(V_r,T_a)
| ! [V_x] : ~ c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(miniscoping,[status(thm)],[f585]) ).
fof(f1547,plain,
! [X0,X1,X2] :
( ~ c_in(c_Pair(X2,X2,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Relation_Oirrefl(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1546]) ).
fof(f1559,plain,
! [X0,X1,X2] : c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1)),
inference(cnf_transformation,[status(thm)],[f592]) ).
fof(f1561,plain,
! [T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ! [V_x,V_a] :
( ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(miniscoping,[status(thm)],[f594]) ).
fof(f1562,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1561]) ).
fof(f1563,plain,
! [T_a,V_r] :
( ~ c_Relation_Oantisym(V_r,T_a)
| ! [V_x,V_y] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| V_x = V_y ) ),
inference(miniscoping,[status(thm)],[f595]) ).
fof(f1564,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1))
| X3 = X2
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Relation_Oantisym(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1563]) ).
fof(f1577,plain,
! [T_a,V_r] :
( ~ c_Wellfounded_Owf(V_r,T_a)
| ! [V_a] : ~ c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(miniscoping,[status(thm)],[f602]) ).
fof(f1578,plain,
! [X0,X1,X2] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)) ),
inference(cnf_transformation,[status(thm)],[f1577]) ).
fof(f1583,plain,
! [T_a,V_r] :
( ~ c_Relation_Osym(V_r,T_a)
| ! [V_y,V_x] :
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ),
inference(miniscoping,[status(thm)],[f605]) ).
fof(f1584,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Osym(X3,X2)
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f1583]) ).
fof(f1587,plain,
! [V_a,T_a,V_r,T_b,V_b] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| ! [V_c,T_c,V_s] :
( ~ c_in(c_Pair(V_b,V_c,T_b,T_c),V_s,tc_prod(T_b,T_c))
| c_in(c_Pair(V_a,V_c,T_a,T_c),c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),tc_prod(T_a,T_c)) ) ),
inference(miniscoping,[status(thm)],[f607]) ).
fof(f1588,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_in(c_Pair(X0,X5,X2,X6),c_Relation_Orel__comp(X4,X7,X2,X3,X6),tc_prod(X2,X6))
| ~ c_in(c_Pair(X1,X5,X3,X6),X7,tc_prod(X3,X6))
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f1587]) ).
fof(f1595,plain,
! [V_x,V_z] :
( V_x = V_z
| ! [V_y] :
( V_x = V_y
| ! [V_L] :
( ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ) ),
inference(miniscoping,[status(thm)],[f612]) ).
fof(f1596,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,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),c_Arrow__Order__Mirabelle_Omktop(X3,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1595]) ).
fof(f1602,plain,
! [V_x,V_y] :
( ! [V_L] : c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_y = V_x
| V_x = V_y ),
inference(miniscoping,[status(thm)],[f617]) ).
fof(f1603,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
fof(f1610,plain,
! [V_xa,V_x] :
( ! [V_L] : c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| V_xa = V_x
| V_xa = V_x ),
inference(miniscoping,[status(thm)],[f622]) ).
fof(f1611,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1610]) ).
fof(f1613,plain,
! [X0,X1] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f624]) ).
fof(f1618,plain,
! [V_r,T_a,V_b] :
( ~ c_in(V_b,c_Wellfounded_Oacc(V_r,T_a),T_a)
| ! [V_a] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_a,c_Wellfounded_Oacc(V_r,T_a),T_a) ) ),
inference(miniscoping,[status(thm)],[f627]) ).
fof(f1619,plain,
! [X0,X1,X2,X3] :
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_in(c_Pair(X3,X0,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X0,c_Wellfounded_Oacc(X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f1618]) ).
fof(f1622,plain,
! [V_A,T_a,V_a] :
( ~ c_in(V_a,V_A,T_a)
| ! [V_b,V_r,T_b] :
( ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_b,c_Relation_OImage(V_r,V_A,T_a,T_b),T_b) ) ),
inference(miniscoping,[status(thm)],[f629]) ).
fof(f1623,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
| ~ c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f1622]) ).
fof(f1628,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X0,X0,X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f632]) ).
fof(f1629,plain,
! [V_A,T_a,V_r] :
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ! [V_y] :
( ! [V_x] : ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f633]) ).
fof(f1630,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Equiv__Relations_Oequiv(X1,X4,X2)
| ~ c_in(c_Pair(X3,X0,X2,X2),X4,tc_prod(X2,X2))
| c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1629]) ).
fof(f1633,plain,
! [V_a,V_r,T_b,T_a] :
( ! [V_x] : ~ c_in(c_Pair(V_x,V_a,T_b,T_a),V_r,tc_prod(T_b,T_a))
| c_in(V_a,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f635]) ).
fof(f1634,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X1,c_Relation_ORange(X4,X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f1633]) ).
fof(f1639,plain,
! [V_a,V_r,T_a,T_b] :
( ! [V_b] : ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b))
| c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
inference(miniscoping,[status(thm)],[f638]) ).
fof(f1640,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f1639]) ).
fof(f1649,plain,
! [V_A,T_a,V_r] :
( ~ c_Relation_Orefl__on(V_A,V_r,T_a)
| ! [V_y] :
( ! [V_x] : ~ c_in(c_Pair(V_x,V_y,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_y,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f643]) ).
fof(f1650,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Orefl__on(X1,X3,X2)
| c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1649]) ).
fof(f1662,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)],[f651]) ).
fof(f1663,plain,
( v_a____ = v_b_H____
| v_b____ = v_a_H____
| ~ 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)],[f652]) ).
fof(f1664,plain,
( v_a____ = v_b_H____
| v_b____ = v_a_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))
| 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)],[f653]) ).
fof(f1665,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)],[f654]) ).
fof(f1666,plain,
! [X0,X1,X2] :
( c_in(X1,X0,X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1665]) ).
fof(f1667,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)],[f655]) ).
fof(f1668,plain,
! [X0,X1,X2] :
( ~ c_in(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1667]) ).
fof(f1669,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))
| v_a____ = v_b_H____
| v_b____ != v_a_H____ ),
inference(cnf_transformation,[status(thm)],[f656]) ).
fof(f1670,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))
| v_a____ = v_b_H____
| v_b____ != v_a_H____ ),
inference(cnf_transformation,[status(thm)],[f657]) ).
fof(f1671,plain,
( v_b____ = v_a_H____
| ~ 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))
| v_a____ != v_b_H____ ),
inference(cnf_transformation,[status(thm)],[f658]) ).
fof(f1672,plain,
( v_b____ = v_a_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))
| 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(cnf_transformation,[status(thm)],[f659]) ).
fof(f1674,plain,
! [X0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f661]) ).
fof(f1675,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)],[f662]) ).
fof(f1676,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)],[f663]) ).
fof(f1678,plain,
v_a____ != v_b____,
inference(cnf_transformation,[status(thm)],[f665]) ).
fof(f1679,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [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_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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)],[f666]) ).
fof(f1680,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X2,X3,X0,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)))
| 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))
| X1 = X0
| ~ c_in(c_Pair(X1,X0,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(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X2,X3,X0,X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f1679]) ).
fof(f1681,plain,
! [V_b,V_a] :
( V_a = V_b
| ! [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_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_b)),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_b,V_a,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)],[f667]) ).
fof(f1682,plain,
! [X0,X1,X2,X3] :
( ~ 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(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)))
| X0 = X1
| ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__CHAINED__1(X3,X2,X1,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(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(X3,v_sko__CHAINED__1(X3,X2,X1,X0)),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(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cnf_transformation,[status(thm)],[f1681]) ).
fof(f1683,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [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_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P_H,v_sko__CHAINED__1(V_P,V_P_H,V_a,V_b)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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)],[f668]) ).
fof(f1684,plain,
! [X0,X1,X2,X3] :
( ~ 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(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__CHAINED__1(X3,X2,X0,X1)),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(X3,X2,X0,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(X3),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(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 = X1 ),
inference(cnf_transformation,[status(thm)],[f1683]) ).
fof(f1689,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)],[f672]) ).
fof(f1690,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)],[f673]) ).
fof(f1699,plain,
! [T_1] :
( ~ class_Lattices_Oboolean__algebra(T_1)
| ! [T_2] : class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
inference(miniscoping,[status(thm)],[f678]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1699]) ).
fof(f1711,plain,
class_Lattices_Oupper__semilattice(tc_bool),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f1712,plain,
class_Lattices_Olower__semilattice(tc_bool),
inference(cnf_transformation,[status(thm)],[f685]) ).
fof(f1714,plain,
class_Lattices_Obounded__lattice(tc_bool),
inference(cnf_transformation,[status(thm)],[f687]) ).
fof(f1715,plain,
class_Lattices_Oboolean__algebra(tc_bool),
inference(cnf_transformation,[status(thm)],[f688]) ).
fof(f1717,plain,
class_Lattices_Olattice(tc_bool),
inference(cnf_transformation,[status(thm)],[f690]) ).
fof(f1724,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(f1725,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)],[f1724]) ).
fof(f1726,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)],[f1724]) ).
fof(f1727,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(f1728,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)],[f1727]) ).
fof(f1730,definition,
( sQ2_spl
<=> v_b____ = v_a_H____ ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1731,plain,
( ~ sQ2_spl
| v_b____ = v_a_H____ ),
inference(component_clause,[status(thm)],[f1730]) ).
fof(f1733,definition,
( sQ3_spl
<=> v_a____ = v_b_H____ ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1734,plain,
( ~ sQ3_spl
| v_a____ = v_b_H____ ),
inference(component_clause,[status(thm)],[f1733]) ).
fof(f1736,plain,
( sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1663,f1724,f1727,f1730,f1733]) ).
fof(f1737,plain,
( sQ3_spl
| sQ2_spl
| ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f1664,f1727,f1724,f1730,f1733]) ).
fof(f1738,plain,
( ~ sQ1_spl
| sQ0_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1669,f1730,f1733,f1724,f1727]) ).
fof(f1739,plain,
( ~ sQ0_spl
| sQ1_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1670,f1730,f1733,f1727,f1724]) ).
fof(f1740,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1671,f1733,f1724,f1727,f1730]) ).
fof(f1741,plain,
( sQ2_spl
| ~ sQ0_spl
| sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1672,f1733,f1727,f1724,f1730]) ).
fof(f1742,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1689,f1724,f1727]) ).
fof(f1743,plain,
( sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f1690,f1727,f1724]) ).
fof(f1744,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f1603]) ).
fof(f1745,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f1611]) ).
fof(f1746,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ c_in(c_Pair(v_b____,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(forward_demodulation,[status(thm)],[f1731,f1726]) ).
fof(f1747,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ c_in(c_Pair(v_b____,v_a____,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(forward_demodulation,[status(thm)],[f1734,f1746]) ).
fof(f1748,plain,
! [X0] :
( ~ sQ2_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_demodulation,[status(thm)],[f1731,f1674]) ).
fof(f1749,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| c_in(c_Pair(v_b____,v_a____,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(forward_demodulation,[status(thm)],[f1734,f1748]) ).
fof(f1774,plain,
! [X0,X1,X2] :
( X1 = c_Set_Oinsert(X0,X1,X2)
| ~ c_in(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f766,f1138]) ).
fof(f1782,plain,
! [X0] :
( ~ sQ2_spl
| ~ c_in(c_Pair(v_b____,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(forward_demodulation,[status(thm)],[f1731,f1662]) ).
fof(f1783,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_demodulation,[status(thm)],[f1734,f1782]) ).
fof(f1804,plain,
( ~ sQ1_spl
| c_in(v_a____,c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1640,f1728]) ).
fof(f1807,plain,
( ~ sQ1_spl
| c_in(v_b____,c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1634,f1728]) ).
fof(f1832,plain,
( ~ sQ1_spl
| ~ c_Relation_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1584,f1728]) ).
fof(f1834,definition,
( sQ4_spl
<=> c_in(c_Pair(v_b____,v_a____,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,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1837,definition,
( sQ5_spl
<=> c_Relation_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1840,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1832,f1834,f1837,f1727]) ).
fof(f1841,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| c_in(c_Pair(v_b____,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(forward_demodulation,[status(thm)],[f1731,f1725]) ).
fof(f1842,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| c_in(c_Pair(v_b____,v_a____,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(forward_demodulation,[status(thm)],[f1734,f1841]) ).
fof(f1886,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1562,f1728]) ).
fof(f1888,definition,
( sQ8_spl
<=> c_Wellfounded_Owf(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1891,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1886,f1834,f1888,f1727]) ).
fof(f1892,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(v_b____,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,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)) ),
inference(resolution,[status(thm)],[f1542,f1728]) ).
fof(f1895,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,v_a____,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,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)],[f1542,f1728]) ).
fof(f1897,definition,
! [X0] :
( sQ9_spl
<=> ( ~ c_in(c_Pair(X0,v_a____,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(X0,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,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1900,definition,
( sQ10_spl
<=> c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1903,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1895,f1897,f1900,f1727]) ).
fof(f1904,definition,
! [X0] :
( sQ11_spl
<=> ( ~ c_in(c_Pair(v_b____,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(v_a____,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)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1907,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1892,f1904,f1900,f1727]) ).
fof(f1959,plain,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool),
inference(resolution,[status(thm)],[f1712,f758]) ).
fof(f2001,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,v_a____,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,v_F(v_P____),X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1588,f1728]) ).
fof(f2066,plain,
! [X0] : X0 = c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool),
inference(resolution,[status(thm)],[f703,f1711]) ).
fof(f2156,plain,
! [X0] : class_Lattices_Oboolean__algebra(tc_fun(X0,tc_bool)),
inference(resolution,[status(thm)],[f1700,f1715]) ).
fof(f2158,plain,
! [X0,X1] : class_Lattices_Oboolean__algebra(tc_fun(X0,tc_fun(X1,tc_bool))),
inference(resolution,[status(thm)],[f2156,f1700]) ).
fof(f2180,plain,
! [X0] :
( ~ sQ1_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)))
| ~ 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____,v_b____,v_a____)),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)))
| c_in(c_Pair(v_b____,v_a____,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))
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1680,f1728]) ).
fof(f2181,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(X0,v_P____,v_b____,v_a____)),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)))
| c_in(c_Pair(v_b____,v_a____,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(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2182,plain,
! [X0] :
( ~ sQ16_spl
| ~ 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(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(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____,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2181]) ).
fof(f2184,definition,
( sQ17_spl
<=> v_a____ = v_b____ ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2185,plain,
( ~ sQ17_spl
| v_a____ = v_b____ ),
inference(component_clause,[status(thm)],[f2184]) ).
fof(f2187,definition,
( sQ18_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,[sQ18_spl])],[split_symbol_definition]) ).
fof(f2189,plain,
( sQ18_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)],[f2187]) ).
fof(f2190,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f2180,f2181,f2184,f2187,f1727]) ).
fof(f2191,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2189,f1676]) ).
fof(f2192,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f2191]) ).
fof(f2285,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1628,f1807]) ).
fof(f2288,plain,
( ~ sQ1_spl
| c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f1628,f1728]) ).
fof(f2308,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2285,f1542]) ).
fof(f2309,plain,
( ~ sQ1_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2285,f1542]) ).
fof(f2310,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2285,f1542]) ).
fof(f2311,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2285,f1562]) ).
fof(f2325,plain,
( ~ sQ1_spl
| c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2285,f1628]) ).
fof(f2328,definition,
( sQ19_spl
<=> c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f2331,definition,
( sQ20_spl
<=> c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f2334,plain,
( ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2311,f2328,f2331,f1727]) ).
fof(f2335,definition,
( sQ21_spl
<=> c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f2337,plain,
( sQ21_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2335]) ).
fof(f2338,plain,
( ~ sQ1_spl
| ~ sQ21_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f2309,f2328,f2335,f1727]) ).
fof(f2342,definition,
! [X0] :
( sQ22_spl
<=> ( ~ c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2345,plain,
( ~ sQ1_spl
| ~ sQ21_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f2308,f2342,f2335,f1727]) ).
fof(f2346,definition,
! [X0] :
( sQ23_spl
<=> ( ~ c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2349,plain,
( ~ sQ1_spl
| ~ sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f2310,f2346,f2335,f1727]) ).
fof(f2350,definition,
( sQ24_spl
<=> c_Relation_Osym(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2352,plain,
( sQ24_spl
| ~ c_Relation_Osym(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2350]) ).
fof(f2381,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_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_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,v_a____,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)))
| c_in(c_Pair(v_a____,v_b____,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))
| v_b____ = v_a____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1842,f1680]) ).
fof(f2399,definition,
! [X0] :
( sQ25_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,v_a____,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)))
| c_in(c_Pair(v_a____,v_b____,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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,v_a____,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(f2400,plain,
! [X0] :
( ~ sQ25_spl
| ~ 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(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),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(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(X0,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2399]) ).
fof(f2402,definition,
( 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))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f2404,plain,
( 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))) ),
inference(component_clause,[status(thm)],[f2402]) ).
fof(f2405,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ26_spl
| sQ17_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f2381,f2399,f2184,f2402,f1733,f1730,f1724]) ).
fof(f2409,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2337,f1434]) ).
fof(f2410,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f2409]) ).
fof(f2411,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2185,f1678]) ).
fof(f2412,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f2411]) ).
fof(f2577,definition,
( sQ36_spl
<=> c_Relation_Otrans(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f2579,plain,
( sQ36_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2577]) ).
fof(f2593,definition,
( sQ39_spl
<=> c_Relation_Osym(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f2595,plain,
( sQ39_spl
| ~ c_Relation_Osym(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2593]) ).
fof(f2602,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2579,f1434]) ).
fof(f2603,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f2602]) ).
fof(f2710,definition,
( sQ47_spl
<=> c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f2712,plain,
( sQ47_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2710]) ).
fof(f2734,definition,
( sQ52_spl
<=> c_Relation_Osym(c_Relation_OId__on(c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2736,plain,
( sQ52_spl
| ~ c_Relation_Osym(c_Relation_OId__on(c_Relation_ORange(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2734]) ).
fof(f2740,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2712,f1434]) ).
fof(f2741,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f2740]) ).
fof(f2766,plain,
! [X0,X1,X2,X3] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X3),
inference(resolution,[status(thm)],[f1124,f1666]) ).
fof(f2869,definition,
( sQ54_spl
<=> c_Relation_Osym(c_Relation_OId__on(c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f2871,plain,
( sQ54_spl
| ~ c_Relation_Osym(c_Relation_OId__on(c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2869]) ).
fof(f2877,definition,
( sQ56_spl
<=> c_Relation_Otrans(c_Relation_OId__on(c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f2879,plain,
( sQ56_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_ODomain(v_F(v_P_H____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f2877]) ).
fof(f2898,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2879,f1434]) ).
fof(f2899,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f2898]) ).
fof(f2914,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),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(X0),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)))
| ~ c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f1684,f1842]) ).
fof(f2915,definition,
! [X0] :
( sQ60_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),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(X0),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))) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2916,plain,
! [X0] :
( ~ sQ60_spl
| c_in(c_Pair(v_a____,v_b____,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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P_H____,v_a____,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)))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(X0,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f2915]) ).
fof(f2918,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ60_spl
| ~ sQ26_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f2914,f2184,f2402,f2915,f1733,f1730,f1724]) ).
fof(f2919,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2404,f1675]) ).
fof(f2920,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f2919]) ).
fof(f3184,definition,
( sQ72_spl
<=> v_b____ = v_b____ ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f3354,plain,
! [X0] : X0 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool),
inference(resolution,[status(thm)],[f1011,f1715]) ).
fof(f3500,definition,
( sQ77_spl
<=> c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f3502,plain,
( sQ77_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(component_clause,[status(thm)],[f3500]) ).
fof(f3517,definition,
( sQ80_spl
<=> c_Relation_Osym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f3519,plain,
( sQ80_spl
| ~ c_Relation_Osym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(component_clause,[status(thm)],[f3517]) ).
fof(f3521,plain,
( sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3502,f1434]) ).
fof(f3522,plain,
sQ77_spl,
inference(contradiction_clause,[status(thm)],[f3521]) ).
fof(f3543,plain,
( ~ sQ60_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))
| 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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1676,f2916]) ).
fof(f3545,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(resolution,[status(thm)],[f1676,f1668]) ).
fof(f3547,definition,
( sQ81_spl
<=> c_in(c_Pair(v_b____,v_a____,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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f3548,plain,
( ~ sQ81_spl
| c_in(c_Pair(v_b____,v_a____,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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f3547]) ).
fof(f3550,definition,
( sQ82_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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f3551,plain,
( ~ sQ82_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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f3550]) ).
fof(f3553,plain,
( ~ sQ60_spl
| sQ1_spl
| sQ82_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f3543,f3547,f3550,f1727,f2915]) ).
fof(f3581,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ81_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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3548,f1783]) ).
fof(f3681,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ81_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)))
| ~ c_in(c_Pair(v_b____,v_a____,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_b____)),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(resolution,[status(thm)],[f3581,f2400]) ).
fof(f3721,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ81_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f3681,f1727,f3547,f2187,f1733,f1730,f2399]) ).
fof(f3733,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ82_spl
| c_in(c_Pair(v_b____,v_a____,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_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3551,f1749]) ).
fof(f3761,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ82_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f3733,f3547,f3550,f1733,f1730]) ).
fof(f3764,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),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(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),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)))
| ~ 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____ ),
inference(resolution,[status(thm)],[f1728,f1684]) ).
fof(f3766,plain,
( ~ sQ1_spl
| c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1728,f1619]) ).
fof(f3767,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1728,f1543]) ).
fof(f3784,plain,
( ~ sQ1_spl
| hBOOL(hAPP(v_F(v_P____),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f1728,f1668]) ).
fof(f3787,definition,
( sQ108_spl
<=> c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f3789,plain,
( sQ108_spl
| ~ c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(component_clause,[status(thm)],[f3787]) ).
fof(f3790,definition,
( sQ109_spl
<=> c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f3793,plain,
( ~ sQ1_spl
| sQ109_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f3766,f3787,f3790,f1727]) ).
fof(f3798,definition,
! [X0] :
( sQ110_spl
<=> ( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),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(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),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))) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f3799,plain,
! [X0] :
( ~ sQ110_spl
| ~ 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(v_b____,v_a____,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(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_a____)),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(X0,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f3798]) ).
fof(f3801,plain,
( ~ sQ1_spl
| sQ110_spl
| ~ sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f3764,f2184,f2187,f3798,f1727]) ).
fof(f3805,plain,
( ~ sQ1_spl
| c_in(v_b____,c_Wellfounded_Oacc(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,c_Wellfounded_Oacc(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3767,f1619]) ).
fof(f3808,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3767,f1542]) ).
fof(f3809,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3767,f1542]) ).
fof(f3810,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3767,f1562]) ).
fof(f3811,plain,
( ~ sQ1_spl
| ~ c_Relation_Osym(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3767,f1584]) ).
fof(f3822,plain,
( ~ sQ1_spl
| c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Set_Oinsert(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3767,f1774]) ).
fof(f3826,definition,
( sQ111_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f3827,plain,
( ~ sQ111_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f3826]) ).
fof(f3829,definition,
( sQ112_spl
<=> c_Relation_Osym(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f3832,plain,
( ~ sQ1_spl
| ~ sQ112_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f3811,f3826,f3829,f1727]) ).
fof(f3833,definition,
( sQ113_spl
<=> c_in(v_a____,c_Wellfounded_Oacc(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f3836,definition,
( sQ114_spl
<=> c_in(v_b____,c_Wellfounded_Oacc(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f3839,plain,
( ~ sQ1_spl
| sQ114_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f3805,f3833,f3836,f1727]) ).
fof(f3842,definition,
! [X0] :
( sQ115_spl
<=> ( ~ c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f3845,definition,
( sQ116_spl
<=> c_Relation_Otrans(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f3848,plain,
( ~ sQ1_spl
| ~ sQ116_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f3809,f3842,f3845,f1727]) ).
fof(f3849,definition,
! [X0] :
( sQ117_spl
<=> ( ~ c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f3852,plain,
( ~ sQ1_spl
| ~ sQ116_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f3808,f3849,f3845,f1727]) ).
fof(f3853,definition,
( sQ118_spl
<=> c_Wellfounded_Owf(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f3856,plain,
( ~ sQ1_spl
| ~ sQ118_spl
| ~ sQ111_spl ),
inference(split_clause,[status(thm)],[f3810,f3826,f3853,f1727]) ).
fof(f3911,plain,
! [X0] : c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,X0),
inference(resolution,[status(thm)],[f3545,f1666]) ).
fof(f3919,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2001,f3767]) ).
fof(f3920,plain,
! [X0,X1] :
( ~ sQ1_spl
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X1,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = X0 ),
inference(resolution,[status(thm)],[f2001,f1745]) ).
fof(f3921,plain,
! [X0] :
( ~ sQ1_spl
| v_a____ = X0
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2001,f1613]) ).
fof(f3922,plain,
! [X0,X1] :
( ~ sQ1_spl
| X0 = v_a____
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2001,f1744]) ).
fof(f3966,plain,
( ~ sQ1_spl
| hBOOL(hAPP(c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
inference(resolution,[status(thm)],[f1804,f1668]) ).
fof(f4000,plain,
( ~ sQ1_spl
| hBOOL(hAPP(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
inference(resolution,[status(thm)],[f1807,f1668]) ).
fof(f4002,plain,
! [X0,X1] :
( ~ sQ1_spl
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(X1,tc_bool)),v_a____)) ),
inference(resolution,[status(thm)],[f3966,f859]) ).
fof(f4023,plain,
! [X0,X1] :
( ~ sQ1_spl
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(X1,tc_bool)),v_b____)) ),
inference(resolution,[status(thm)],[f4000,f859]) ).
fof(f4141,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2288,f1542]) ).
fof(f4143,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2288,f1542]) ).
fof(f4144,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2288,f1562]) ).
fof(f4145,plain,
( ~ sQ1_spl
| ~ c_Relation_Osym(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2288,f1584]) ).
fof(f4146,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),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),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2288,f1623]) ).
fof(f4160,plain,
( ~ sQ1_spl
| c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ),
inference(resolution,[status(thm)],[f2288,f1628]) ).
fof(f4161,definition,
( sQ119_spl
<=> c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f4164,definition,
( sQ120_spl
<=> c_Relation_Osym(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f4166,plain,
( sQ120_spl
| ~ c_Relation_Osym(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f4164]) ).
fof(f4167,plain,
( ~ sQ1_spl
| ~ sQ120_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f4145,f4161,f4164,f1727]) ).
fof(f4168,definition,
! [X0] :
( sQ121_spl
<=> ( ~ c_in(c_Pair(X0,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(X0,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f4171,definition,
( sQ122_spl
<=> c_Relation_Otrans(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f4173,plain,
( sQ122_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f4171]) ).
fof(f4174,plain,
( ~ sQ1_spl
| ~ sQ122_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f4141,f4168,f4171,f1727]) ).
fof(f4175,definition,
( sQ123_spl
<=> c_Wellfounded_Owf(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f4178,plain,
( ~ sQ1_spl
| ~ sQ123_spl
| ~ sQ119_spl ),
inference(split_clause,[status(thm)],[f4144,f4161,f4175,f1727]) ).
fof(f4186,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(forward_demodulation,[status(thm)],[f1230,f4146]) ).
fof(f4188,definition,
! [X0] :
( sQ125_spl
<=> ( ~ c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f4191,plain,
( ~ sQ1_spl
| ~ sQ122_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f4143,f4188,f4171,f1727]) ).
fof(f4193,plain,
( sQ122_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4173,f1434]) ).
fof(f4194,plain,
sQ122_spl,
inference(contradiction_clause,[status(thm)],[f4193]) ).
fof(f4195,plain,
! [X0,X1] :
( ~ sQ1_spl
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X0,tc_fun(X1,tc_bool)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f3784,f859]) ).
fof(f4196,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),X0) ),
inference(resolution,[status(thm)],[f3784,f1666]) ).
fof(f4216,plain,
! [X0] :
( ~ sQ1_spl
| c_Set_Oinsert(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),X0) = v_F(v_P____) ),
inference(resolution,[status(thm)],[f4196,f1774]) ).
fof(f4255,plain,
( ~ sQ110_spl
| c_in(c_Pair(v_b____,v_a____,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_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),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____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3799,f3911]) ).
fof(f4256,definition,
( sQ126_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____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f4257,plain,
( ~ sQ126_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____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f4256]) ).
fof(f4259,definition,
( sQ127_spl
<=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f4260,plain,
( ~ sQ127_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f4259]) ).
fof(f4262,plain,
( ~ sQ110_spl
| sQ4_spl
| sQ127_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f4255,f4256,f4259,f1834,f3798]) ).
fof(f4264,plain,
( ~ sQ127_spl
| c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f4260,f1619]) ).
fof(f4267,plain,
! [X0] :
( ~ sQ127_spl
| ~ c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4260,f1542]) ).
fof(f4268,plain,
! [X0] :
( ~ sQ127_spl
| ~ c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4260,f1542]) ).
fof(f4269,plain,
( ~ sQ127_spl
| ~ c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),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____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4260,f1562]) ).
fof(f4270,plain,
( ~ sQ127_spl
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),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____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4260,f1584]) ).
fof(f4284,definition,
( sQ128_spl
<=> c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f4287,plain,
( ~ sQ127_spl
| ~ sQ128_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f4270,f4256,f4284,f4259]) ).
fof(f4288,definition,
( sQ129_spl
<=> c_Wellfounded_Owf(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f4291,plain,
( ~ sQ127_spl
| ~ sQ129_spl
| ~ sQ126_spl ),
inference(split_clause,[status(thm)],[f4269,f4256,f4288,f4259]) ).
fof(f4292,definition,
! [X0] :
( sQ130_spl
<=> ( ~ c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f4295,definition,
( sQ131_spl
<=> c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f4298,plain,
( ~ sQ127_spl
| ~ sQ131_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f4267,f4292,f4295,f4259]) ).
fof(f4299,definition,
! [X0] :
( sQ132_spl
<=> ( ~ c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f4302,plain,
( ~ sQ127_spl
| ~ sQ131_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f4268,f4299,f4295,f4259]) ).
fof(f4303,definition,
( sQ133_spl
<=> c_in(v_a____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f4306,definition,
( sQ134_spl
<=> c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f4309,plain,
( ~ sQ127_spl
| sQ134_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f4264,f4303,f4306,f4259]) ).
fof(f4310,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2352,f1452]) ).
fof(f4311,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f4310]) ).
fof(f4314,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2736,f1452]) ).
fof(f4315,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f4314]) ).
fof(f4316,plain,
( sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2595,f1452]) ).
fof(f4317,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f4316]) ).
fof(f4318,plain,
( sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4166,f1452]) ).
fof(f4319,plain,
sQ120_spl,
inference(contradiction_clause,[status(thm)],[f4318]) ).
fof(f4320,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2871,f1452]) ).
fof(f4321,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f4320]) ).
fof(f4322,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3519,f1452]) ).
fof(f4323,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f4322]) ).
fof(f4335,plain,
( ~ sQ16_spl
| ~ sQ126_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)))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4257,f2182]) ).
fof(f4336,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ126_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4257,f1749]) ).
fof(f4337,plain,
( ~ sQ126_spl
| c_in(v_a____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,c_Wellfounded_Oacc(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f4257,f1619]) ).
fof(f4340,plain,
! [X0] :
( ~ sQ126_spl
| ~ c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4257,f1542]) ).
fof(f4341,plain,
! [X0] :
( ~ sQ126_spl
| ~ c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4257,f1542]) ).
fof(f4342,plain,
( ~ sQ126_spl
| ~ c_Relation_Osym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4257,f1584]) ).
fof(f4356,plain,
( ~ sQ126_spl
| sQ133_spl
| ~ sQ134_spl ),
inference(split_clause,[status(thm)],[f4337,f4306,f4303,f4256]) ).
fof(f4357,plain,
( ~ sQ16_spl
| ~ sQ126_spl
| ~ sQ18_spl
| ~ sQ127_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f4335,f1834,f4259,f2187,f4256,f2181]) ).
fof(f4358,plain,
( ~ sQ126_spl
| ~ sQ128_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f4342,f4259,f4284,f4256]) ).
fof(f4359,definition,
! [X0] :
( sQ135_spl
<=> ( ~ c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f4362,plain,
( ~ sQ126_spl
| ~ sQ131_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f4341,f4359,f4295,f4256]) ).
fof(f4363,definition,
! [X0] :
( sQ136_spl
<=> ( ~ c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f4366,plain,
( ~ sQ126_spl
| ~ sQ131_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f4340,f4363,f4295,f4256]) ).
fof(f4617,plain,
! [X0] :
( ~ sQ1_spl
| ~ 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(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____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____)),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____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1682,f4196]) ).
fof(f4618,definition,
! [X0] :
( sQ148_spl
<=> ( ~ 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(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_b____)),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____,X0,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f4621,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| sQ17_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f4617,f4618,f2184,f2187,f1727]) ).
fof(f4702,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0) ),
inference(paramodulation,[status(thm)],[f3822,f2766]) ).
fof(f4738,plain,
! [X0,X1] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1)
| ~ c_lessequals(v_F(v_P____),X0,tc_fun(X1,tc_bool)) ),
inference(paramodulation,[status(thm)],[f4216,f773]) ).
fof(f4790,plain,
! [X0,X1] :
( ~ sQ1_spl
| hBOOL(hAPP(c_Set_Oinsert(X0,v_F(v_P____),X1),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f776,f3784]) ).
fof(f4828,plain,
! [X0] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool) = X0
| ~ class_Lattices_Oboolean__algebra(tc_bool) ),
inference(resolution,[status(thm)],[f901,f3354]) ).
fof(f4830,plain,
! [X0,X1] :
( X1 != c_HOL_Ouminus__class_Ouminus(X0,tc_bool)
| X0 = c_HOL_Ouminus__class_Ouminus(X1,tc_bool)
| ~ class_Lattices_Oboolean__algebra(tc_bool) ),
inference(paramodulation,[status(thm)],[f3354,f901]) ).
fof(f4834,plain,
! [X0,X1] :
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(equality_resolution,[status(thm)],[f901]) ).
fof(f4835,definition,
( sQ149_spl
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f4837,plain,
( sQ149_spl
| ~ class_Lattices_Oboolean__algebra(tc_bool) ),
inference(component_clause,[status(thm)],[f4835]) ).
fof(f4838,definition,
! [X0] :
( sQ150_spl
<=> c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool) = X0 ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f4841,plain,
( sQ150_spl
| ~ sQ149_spl ),
inference(split_clause,[status(thm)],[f4828,f4835,f4838]) ).
fof(f4843,definition,
! [X0] :
( sQ151_spl
<=> ~ class_Lattices_Oboolean__algebra(X0) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f4844,plain,
! [X0] :
( ~ sQ151_spl
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(component_clause,[status(thm)],[f4843]) ).
fof(f4846,definition,
! [X1] :
( sQ152_spl
<=> X1 = X1 ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f4849,plain,
( sQ152_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f4834,f4843,f4846]) ).
fof(f4850,definition,
! [X0,X1] :
( sQ153_spl
<=> ( X1 != c_HOL_Ouminus__class_Ouminus(X0,tc_bool)
| X0 = c_HOL_Ouminus__class_Ouminus(X1,tc_bool) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f4853,plain,
( sQ153_spl
| ~ sQ149_spl ),
inference(split_clause,[status(thm)],[f4830,f4835,f4850]) ).
fof(f4856,plain,
( sQ149_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4837,f1715]) ).
fof(f4857,plain,
sQ149_spl,
inference(contradiction_clause,[status(thm)],[f4856]) ).
fof(f4858,plain,
( ~ sQ151_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2158,f4844]) ).
fof(f4862,plain,
~ sQ151_spl,
inference(contradiction_clause,[status(thm)],[f4858]) ).
fof(f5009,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(X0,v_F(v_P____),X1),X2) ),
inference(resolution,[status(thm)],[f4790,f1666]) ).
fof(f5179,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f3920,f1578]) ).
fof(f5183,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Relation_Otrans(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f3920,f1542]) ).
fof(f5191,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ c_Relation_Orefl__on(X1,c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X2,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f3920,f1650]) ).
fof(f5194,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ c_Equiv__Relations_Oequiv(X1,c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X2,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f3920,f1630]) ).
fof(f5195,plain,
! [X0,X1] :
( ~ sQ1_spl
| c_in(v_b____,c_Relation_ORange(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X1,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f3920,f1634]) ).
fof(f5198,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Relation_Oirrefl(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f3920,f1547]) ).
fof(f5202,definition,
! [X0] :
( sQ156_spl
<=> ( ~ c_Relation_Otrans(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f5205,plain,
( ~ sQ1_spl
| sQ156_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f5183,f2184,f5202,f1727]) ).
fof(f5206,definition,
! [X0] :
( sQ157_spl
<=> ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f5209,plain,
( ~ sQ1_spl
| sQ157_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f5179,f2184,f5206,f1727]) ).
fof(f5210,definition,
! [X0] :
( sQ158_spl
<=> X0 = v_a____ ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f5211,plain,
! [X0] :
( ~ sQ158_spl
| v_a____ = X0 ),
inference(component_clause,[status(thm)],[f5210]) ).
fof(f5213,definition,
! [X1,X2] :
( sQ159_spl
<=> ( ~ c_Equiv__Relations_Oequiv(X1,c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X2,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f5216,plain,
( ~ sQ1_spl
| sQ159_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f5194,f5210,f5213,f1727]) ).
fof(f5217,definition,
! [X1] :
( sQ160_spl
<=> c_in(v_b____,c_Relation_ORange(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X1,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f5220,plain,
( ~ sQ1_spl
| sQ160_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f5195,f5210,f5217,f1727]) ).
fof(f5222,definition,
! [X0] :
( sQ161_spl
<=> ~ c_Relation_Oirrefl(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f5225,plain,
( ~ sQ1_spl
| sQ161_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f5198,f2184,f5222,f1727]) ).
fof(f5226,definition,
! [X1,X2] :
( sQ162_spl
<=> ( ~ c_Relation_Orefl__on(X1,c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X2,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(v_b____,X1,tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f5229,plain,
( ~ sQ1_spl
| sQ162_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f5191,f5210,f5226,f1727]) ).
fof(f5230,plain,
( ~ sQ158_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1678,f5211]) ).
fof(f5231,plain,
~ sQ158_spl,
inference(contradiction_clause,[status(thm)],[f5230]) ).
fof(f5496,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3919,f1562]) ).
fof(f5531,definition,
( sQ166_spl
<=> c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f5533,plain,
( sQ166_spl
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f5531]) ).
fof(f5535,definition,
( sQ167_spl
<=> c_Wellfounded_Owf(c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f5538,plain,
( ~ sQ1_spl
| ~ sQ167_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f5496,f5531,f5535,f1727]) ).
fof(f5548,plain,
( sQ166_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5533,f3919]) ).
fof(f5549,plain,
( sQ166_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f5548]) ).
fof(f5860,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ),
inference(resolution,[status(thm)],[f4160,f1562]) ).
fof(f5865,plain,
( ~ sQ1_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ),
inference(resolution,[status(thm)],[f4160,f1542]) ).
fof(f5866,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(X0,c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ),
inference(resolution,[status(thm)],[f4160,f1542]) ).
fof(f5868,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ),
inference(resolution,[status(thm)],[f4160,f1542]) ).
fof(f5885,definition,
( sQ170_spl
<=> c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f5888,definition,
( sQ171_spl
<=> c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f5890,plain,
( sQ171_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(component_clause,[status(thm)],[f5888]) ).
fof(f5891,plain,
( ~ sQ1_spl
| ~ sQ171_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f5865,f5885,f5888,f1727]) ).
fof(f5892,definition,
! [X0] :
( sQ172_spl
<=> ( ~ c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f5895,plain,
( ~ sQ1_spl
| ~ sQ171_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f5868,f5892,f5888,f1727]) ).
fof(f5900,definition,
( sQ174_spl
<=> c_Relation_Osym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f5902,plain,
( sQ174_spl
| ~ c_Relation_Osym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(component_clause,[status(thm)],[f5900]) ).
fof(f5906,definition,
! [X0] :
( sQ175_spl
<=> ( ~ c_in(c_Pair(X0,c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| c_in(c_Pair(X0,c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f5909,plain,
( ~ sQ1_spl
| ~ sQ171_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f5866,f5906,f5888,f1727]) ).
fof(f5911,definition,
( sQ176_spl
<=> c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f5914,plain,
( ~ sQ1_spl
| ~ sQ176_spl
| ~ sQ170_spl ),
inference(split_clause,[status(thm)],[f5860,f5885,f5911,f1727]) ).
fof(f5916,plain,
( sQ171_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5890,f1434]) ).
fof(f5917,plain,
sQ171_spl,
inference(contradiction_clause,[status(thm)],[f5916]) ).
fof(f5918,plain,
! [X0] :
( ~ sQ1_spl
| hBOOL(hAPP(X0,v_a____))
| hBOOL(hAPP(c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
inference(resolution,[status(thm)],[f4002,f855]) ).
fof(f5928,definition,
( sQ177_spl
<=> hBOOL(hAPP(c_Relation_ODomain(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____)) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f5931,definition,
! [X0] :
( sQ178_spl
<=> hBOOL(hAPP(X0,v_a____)) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f5932,plain,
! [X0] :
( ~ sQ178_spl
| hBOOL(hAPP(X0,v_a____)) ),
inference(component_clause,[status(thm)],[f5931]) ).
fof(f5934,plain,
( ~ sQ1_spl
| sQ178_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f5918,f5928,f5931,f1727]) ).
fof(f5964,plain,
! [X0] :
( ~ sQ1_spl
| hBOOL(hAPP(X0,v_b____))
| hBOOL(hAPP(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
inference(resolution,[status(thm)],[f4023,f855]) ).
fof(f5972,definition,
( sQ179_spl
<=> hBOOL(hAPP(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____)) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f5975,definition,
! [X0] :
( sQ180_spl
<=> hBOOL(hAPP(X0,v_b____)) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f5976,plain,
! [X0] :
( ~ sQ180_spl
| hBOOL(hAPP(X0,v_b____)) ),
inference(component_clause,[status(thm)],[f5975]) ).
fof(f5978,plain,
( ~ sQ1_spl
| sQ180_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f5964,f5972,f5975,f1727]) ).
fof(f7198,plain,
! [X0] :
( ~ sQ1_spl
| v_b____ = v_a____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4186,f1745]) ).
fof(f7199,plain,
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_a____,v_b____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4186,f1613]) ).
fof(f7200,plain,
! [X0] :
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f4186,f1744]) ).
fof(f7208,definition,
! [X0] :
( sQ181_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f7211,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f7198,f7208,f2184,f1727]) ).
fof(f7212,definition,
( sQ182_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_a____,v_b____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f7215,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f7199,f7212,f2184,f1727]) ).
fof(f7216,definition,
! [X0] :
( sQ183_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f7219,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f7200,f7216,f2184,f1727]) ).
fof(f7409,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X0,tc_fun(X1,tc_bool)),X2) ),
inference(resolution,[status(thm)],[f4195,f1666]) ).
fof(f7439,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool),
inference(resolution,[status(thm)],[f966,f1717]) ).
fof(f7458,plain,
! [X0,X1] : X0 = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool),
inference(resolution,[status(thm)],[f897,f1717]) ).
fof(f7462,plain,
! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool),tc_bool) = X0,
inference(paramodulation,[status(thm)],[f1959,f7458]) ).
fof(f7606,plain,
( ~ sQ1_spl
| c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
| ~ c_Relation_Oantisym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f1564,f4160]) ).
fof(f7607,plain,
( ~ sQ1_spl
| v_b____ = v_b____
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1564,f3919]) ).
fof(f7608,plain,
( ~ sQ1_spl
| v_b____ = v_a____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1564,f4702]) ).
fof(f7611,plain,
! [X0,X1] :
( ~ sQ1_spl
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X0,tc_fun(X1,tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X0,tc_fun(X1,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1564,f7409]) ).
fof(f7612,plain,
! [X0,X1] :
( ~ sQ1_spl
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(X0,v_F(v_P____),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Set_Oinsert(X0,v_F(v_P____),X1),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1564,f5009]) ).
fof(f7613,plain,
( ~ sQ1_spl
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,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_Relation_Oantisym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1564,f4196]) ).
fof(f7615,plain,
( ~ sQ126_spl
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f1564,f4257]) ).
fof(f7628,definition,
( sQ186_spl
<=> c_Relation_Oantisym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f7630,plain,
( sQ186_spl
| ~ c_Relation_Oantisym(c_Relation_OId__on(c_Relation_OId__on(v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(component_clause,[status(thm)],[f7628]) ).
fof(f7631,definition,
( sQ187_spl
<=> c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Pair(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f7634,plain,
( ~ sQ1_spl
| sQ187_spl
| ~ sQ170_spl
| ~ sQ186_spl ),
inference(split_clause,[status(thm)],[f7606,f7628,f5885,f7631,f1727]) ).
fof(f7635,definition,
! [X0,X1] :
( sQ188_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X0,tc_fun(X1,tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X0,tc_fun(X1,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f7638,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f7611,f7635,f2184,f1727]) ).
fof(f7642,definition,
( sQ189_spl
<=> c_Relation_Oantisym(c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f7645,plain,
( ~ sQ1_spl
| sQ72_spl
| ~ sQ166_spl
| ~ sQ189_spl ),
inference(split_clause,[status(thm)],[f7607,f7642,f5531,f3184,f1727]) ).
fof(f7646,definition,
! [X0,X1] :
( sQ190_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Set_Oinsert(X0,v_F(v_P____),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Set_Oinsert(X0,v_F(v_P____),X1),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f7649,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f7612,f7646,f2184,f1727]) ).
fof(f7658,definition,
( sQ192_spl
<=> c_Relation_Oantisym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f7661,plain,
( ~ sQ1_spl
| sQ17_spl
| ~ sQ4_spl
| ~ sQ192_spl ),
inference(split_clause,[status(thm)],[f7613,f7658,f1834,f2184,f1727]) ).
fof(f7662,definition,
( sQ193_spl
<=> c_Relation_Oantisym(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f7665,plain,
( ~ sQ126_spl
| sQ17_spl
| ~ sQ127_spl
| ~ sQ193_spl ),
inference(split_clause,[status(thm)],[f7615,f7662,f4259,f2184,f4256]) ).
fof(f7666,definition,
( sQ194_spl
<=> c_Relation_Oantisym(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f7669,plain,
( ~ sQ1_spl
| sQ17_spl
| ~ sQ111_spl
| ~ sQ194_spl ),
inference(split_clause,[status(thm)],[f7608,f7666,f3826,f2184,f1727]) ).
fof(f7683,plain,
( sQ186_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7630,f1437]) ).
fof(f7684,plain,
sQ186_spl,
inference(contradiction_clause,[status(thm)],[f7683]) ).
fof(f7686,plain,
( sQ174_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5902,f1452]) ).
fof(f7687,plain,
sQ174_spl,
inference(contradiction_clause,[status(thm)],[f7686]) ).
fof(f7727,plain,
! [X0] :
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
inference(resolution,[status(thm)],[f938,f7462]) ).
fof(f7731,plain,
! [X0] :
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
inference(resolution,[status(thm)],[f938,f7458]) ).
fof(f7732,plain,
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(resolution,[status(thm)],[f938,f2066]) ).
fof(f7740,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(paramodulation,[status(thm)],[f7462,f938]) ).
fof(f7741,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool)
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(paramodulation,[status(thm)],[f7458,f938]) ).
fof(f7746,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = X0
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(paramodulation,[status(thm)],[f7439,f938]) ).
fof(f7747,plain,
! [X0] :
( ~ class_Lattices_Obounded__lattice(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = X0
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(paramodulation,[status(thm)],[f2066,f938]) ).
fof(f7749,definition,
! [X0] :
( sQ197_spl
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f7752,definition,
( sQ198_spl
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f7754,plain,
( sQ198_spl
| ~ class_Lattices_Obounded__lattice(tc_bool) ),
inference(component_clause,[status(thm)],[f7752]) ).
fof(f7755,plain,
( ~ sQ198_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f7731,f7749,f7752]) ).
fof(f7756,definition,
! [X0] :
( sQ199_spl
<=> ( c_Orderings_Obot__class_Obot(tc_bool) = X0
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f7759,plain,
( ~ sQ198_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f7747,f7756,f7752]) ).
fof(f7761,definition,
! [X0,X1] :
( sQ200_spl
<=> ( c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f7764,plain,
( ~ sQ198_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f7740,f7761,f7752]) ).
fof(f7767,definition,
( sQ201_spl
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f7770,plain,
( ~ sQ198_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f7732,f7767,f7752]) ).
fof(f7772,definition,
! [X0] :
( sQ202_spl
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f7775,plain,
( ~ sQ198_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f7727,f7772,f7752]) ).
fof(f7779,definition,
! [X0,X1] :
( sQ203_spl
<=> ( c_Orderings_Obot__class_Obot(tc_bool) = X0
| c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f7782,plain,
( ~ sQ198_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f7746,f7779,f7752]) ).
fof(f7785,definition,
! [X0] :
( sQ204_spl
<=> X0 != c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f7786,plain,
! [X0] :
( ~ sQ204_spl
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(component_clause,[status(thm)],[f7785]) ).
fof(f7789,definition,
! [X0,X1] :
( sQ205_spl
<=> ( c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool)
| X0 != c_Orderings_Obot__class_Obot(tc_bool) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f7792,plain,
( ~ sQ198_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f7741,f7789,f7752]) ).
fof(f7794,plain,
( sQ198_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7754,f1714]) ).
fof(f7795,plain,
sQ198_spl,
inference(contradiction_clause,[status(thm)],[f7794]) ).
fof(f7796,plain,
( ~ sQ204_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f7786]) ).
fof(f7797,plain,
~ sQ204_spl,
inference(contradiction_clause,[status(thm)],[f7796]) ).
fof(f7809,plain,
( ~ sQ111_spl
| c_in(v_a____,c_Wellfounded_Oacc(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_b____,c_Wellfounded_Oacc(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f3827,f1619]) ).
fof(f7810,plain,
( ~ sQ111_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3827,f1543]) ).
fof(f7812,plain,
! [X0] :
( ~ sQ111_spl
| ~ c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3827,f1542]) ).
fof(f7813,plain,
! [X0] :
( ~ sQ111_spl
| ~ c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Otrans(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3827,f1542]) ).
fof(f7814,plain,
( ~ sQ111_spl
| ~ c_Relation_Osym(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f3827,f1584]) ).
fof(f7830,definition,
( sQ206_spl
<=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f7834,plain,
( ~ sQ111_spl
| c_in(c_Pair(v_b____,v_a____,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(forward_demodulation,[status(thm)],[f1479,f7810]) ).
fof(f7835,plain,
( ~ sQ111_spl
| sQ113_spl
| ~ sQ114_spl ),
inference(split_clause,[status(thm)],[f7809,f3836,f3833,f3826]) ).
fof(f7837,definition,
! [X0] :
( sQ207_spl
<=> ( ~ c_in(c_Pair(X0,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f7840,plain,
( ~ sQ111_spl
| ~ sQ116_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f7812,f7837,f3845,f3826]) ).
fof(f7841,plain,
( ~ sQ111_spl
| ~ sQ112_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f7814,f7830,f3829,f3826]) ).
fof(f7843,definition,
! [X0] :
( sQ208_spl
<=> ( ~ c_in(c_Pair(v_b____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f7846,plain,
( ~ sQ111_spl
| ~ sQ116_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f7813,f7843,f3845,f3826]) ).
fof(f7852,plain,
! [X0] :
( ~ sQ111_spl
| ~ 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(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____ = v_b____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____)),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(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f7834,f1682]) ).
fof(f7853,plain,
! [X0] :
( ~ sQ111_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,v_b____)),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(X0),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)))
| ~ 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____ = v_b____ ),
inference(resolution,[status(thm)],[f7834,f1684]) ).
fof(f7854,plain,
! [X0] :
( ~ sQ111_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)))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,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)))
| c_in(c_Pair(v_a____,v_b____,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))
| v_b____ = v_a____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f7834,f1680]) ).
fof(f7856,plain,
( ~ sQ111_spl
| 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))
| ~ c_Relation_Oantisym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7834,f1564]) ).
fof(f7857,plain,
( ~ sQ111_spl
| c_in(v_b____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(v_a____,c_Wellfounded_Oacc(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f7834,f1619]) ).
fof(f7860,plain,
! [X0] :
( ~ sQ111_spl
| ~ c_in(c_Pair(X0,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_a____,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)],[f7834,f1542]) ).
fof(f7861,plain,
! [X0] :
( ~ sQ111_spl
| ~ c_in(c_Pair(v_a____,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,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)) ),
inference(resolution,[status(thm)],[f7834,f1542]) ).
fof(f7879,definition,
! [X0] :
( sQ209_spl
<=> ( ~ c_in(c_Pair(v_a____,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(v_b____,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)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f7880,plain,
! [X0] :
( ~ sQ209_spl
| c_in(c_Pair(v_b____,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(v_a____,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)) ),
inference(component_clause,[status(thm)],[f7879]) ).
fof(f7882,plain,
( ~ sQ111_spl
| ~ sQ10_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f7861,f7879,f1900,f3826]) ).
fof(f7883,definition,
! [X0] :
( sQ210_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,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)))
| c_in(c_Pair(v_a____,v_b____,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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f7886,plain,
( ~ sQ111_spl
| ~ sQ18_spl
| sQ17_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f7854,f7883,f2184,f2187,f3826]) ).
fof(f7887,definition,
! [X0] :
( sQ211_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,v_b____)),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(X0),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))) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f7890,plain,
( ~ sQ111_spl
| sQ211_spl
| ~ sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f7853,f2184,f2187,f7887,f3826]) ).
fof(f7891,plain,
( ~ sQ111_spl
| sQ108_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f7857,f3790,f3787,f3826]) ).
fof(f7892,definition,
! [X0] :
( sQ212_spl
<=> ( ~ c_in(c_Pair(X0,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(X0,v_a____,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,[sQ212_spl])],[split_symbol_definition]) ).
fof(f7893,plain,
! [X0] :
( ~ sQ212_spl
| ~ c_in(c_Pair(X0,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(X0,v_a____,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)],[f7892]) ).
fof(f7895,plain,
( ~ sQ111_spl
| ~ sQ10_spl
| sQ212_spl ),
inference(split_clause,[status(thm)],[f7860,f7892,f1900,f3826]) ).
fof(f7896,definition,
! [X0] :
( sQ213_spl
<=> ( ~ 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(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_a____)),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(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f7899,plain,
( ~ sQ111_spl
| ~ sQ18_spl
| sQ17_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f7852,f7896,f2184,f2187,f3826]) ).
fof(f7900,plain,
( ~ sQ111_spl
| sQ17_spl
| ~ sQ1_spl
| ~ sQ192_spl ),
inference(split_clause,[status(thm)],[f7856,f7658,f1727,f2184,f3826]) ).
fof(f8172,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1559,f2001]) ).
fof(f8227,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| c_in(c_Pair(v_b____,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)],[f7880,f4196]) ).
fof(f8230,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ209_spl
| ~ 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(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_b____
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b____,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)) ),
inference(resolution,[status(thm)],[f8227,f1682]) ).
fof(f8231,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ209_spl
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b____,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(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(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_b____ ),
inference(resolution,[status(thm)],[f8227,f1684]) ).
fof(f8232,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ209_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)))
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_b____,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)))
| c_in(c_Pair(v_b____,v_b____,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))
| v_b____ = v_b____
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f8227,f1680]) ).
fof(f8234,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| v_b____ = v_b____
| ~ c_in(c_Pair(v_b____,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_Relation_Oantisym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f8227,f1564]) ).
fof(f8239,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ209_spl
| ~ c_in(c_Pair(X0,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,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)],[f8227,f1542]) ).
fof(f8240,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,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)],[f8227,f1542]) ).
fof(f8241,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ209_spl
| ~ c_in(c_Pair(v_b____,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,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)) ),
inference(resolution,[status(thm)],[f8227,f1542]) ).
fof(f8242,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ c_Relation_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,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)],[f8227,f1584]) ).
fof(f8259,definition,
! [X0] :
( sQ214_spl
<=> ( ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_b____,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)))
| c_in(c_Pair(v_b____,v_b____,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(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f8262,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ sQ18_spl
| sQ72_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f8232,f8259,f3184,f2187,f7879,f1727]) ).
fof(f8263,definition,
( sQ215_spl
<=> c_in(c_Pair(v_b____,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,[sQ215_spl])],[split_symbol_definition]) ).
fof(f8266,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ sQ10_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f8240,f8263,f1900,f7879,f1727]) ).
fof(f8267,definition,
! [X0] :
( sQ216_spl
<=> ( ~ 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(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b____,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)) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f8270,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ sQ18_spl
| sQ72_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f8230,f8267,f3184,f2187,f7879,f1727]) ).
fof(f8271,definition,
! [X0] :
( sQ217_spl
<=> ( ~ c_in(c_Pair(v_b____,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(v_b____,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)) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f8274,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ sQ10_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f8241,f8271,f1900,f7879,f1727]) ).
fof(f8275,definition,
! [X0] :
( sQ218_spl
<=> ( ~ c_in(c_Pair(X0,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(X0,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,[sQ218_spl])],[split_symbol_definition]) ).
fof(f8278,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ sQ10_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f8239,f8275,f1900,f7879,f1727]) ).
fof(f8280,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| ~ sQ5_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f8242,f8263,f1837,f7879,f1727]) ).
fof(f8281,definition,
! [X0] :
( sQ219_spl
<=> ( c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_b____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_b____,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(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,[sQ219_spl])],[split_symbol_definition]) ).
fof(f8284,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| sQ219_spl
| ~ sQ18_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f8231,f3184,f2187,f8281,f7879,f1727]) ).
fof(f8287,plain,
( ~ sQ1_spl
| ~ sQ209_spl
| sQ72_spl
| ~ sQ215_spl
| ~ sQ192_spl ),
inference(split_clause,[status(thm)],[f8234,f7658,f8263,f3184,f7879,f1727]) ).
fof(f8306,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| c_in(c_Pair(v_a____,v_a____,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)],[f7893,f4196]) ).
fof(f8309,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ212_spl
| ~ 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(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____ = v_a____
| ~ c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_a____,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)) ),
inference(resolution,[status(thm)],[f8306,f1682]) ).
fof(f8310,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ212_spl
| c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_a____,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(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(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____ = v_a____ ),
inference(resolution,[status(thm)],[f8306,f1684]) ).
fof(f8311,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ212_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)))
| ~ c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),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)))
| c_in(c_Pair(v_a____,v_a____,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))
| v_a____ = v_a____
| ~ c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f8306,f1680]) ).
fof(f8318,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ212_spl
| ~ c_in(c_Pair(X0,v_a____,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(X0,v_a____,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)],[f8306,f1542]) ).
fof(f8319,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ c_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_a____,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)],[f8306,f1542]) ).
fof(f8320,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ212_spl
| ~ c_in(c_Pair(v_a____,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_Relation_Otrans(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,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)) ),
inference(resolution,[status(thm)],[f8306,f1542]) ).
fof(f8321,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ c_Relation_Osym(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_a____,v_a____,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)],[f8306,f1584]) ).
fof(f8338,definition,
( sQ220_spl
<=> c_in(c_Pair(v_a____,v_a____,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,[sQ220_spl])],[split_symbol_definition]) ).
fof(f8341,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ sQ10_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f8319,f8338,f1900,f7892,f1727]) ).
fof(f8342,definition,
! [X0] :
( sQ221_spl
<=> ( ~ c_in(c_Pair(X0,v_a____,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(X0,v_a____,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,[sQ221_spl])],[split_symbol_definition]) ).
fof(f8345,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ sQ10_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f8318,f8342,f1900,f7892,f1727]) ).
fof(f8346,definition,
( sQ222_spl
<=> v_a____ = v_a____ ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f8350,definition,
! [X0] :
( sQ223_spl
<=> ( c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_a____,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(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,[sQ223_spl])],[split_symbol_definition]) ).
fof(f8353,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| sQ223_spl
| ~ sQ18_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f8310,f8346,f2187,f8350,f7892,f1727]) ).
fof(f8354,definition,
! [X0] :
( sQ224_spl
<=> ( ~ 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(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(v_P____,X0,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(v_P____,X0,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_a____,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)) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f8357,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ sQ18_spl
| sQ222_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f8309,f8354,f8346,f2187,f7892,f1727]) ).
fof(f8359,definition,
! [X0] :
( sQ225_spl
<=> ( ~ c_in(c_Pair(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),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)))
| c_in(c_Pair(v_a____,v_a____,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(v_a____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X0,v_sko__CHAINED__1(X0,v_P____,v_a____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f8362,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ sQ18_spl
| sQ222_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f8311,f8359,f8346,f2187,f7892,f1727]) ).
fof(f8363,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ sQ5_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f8321,f8338,f1837,f7892,f1727]) ).
fof(f8366,definition,
! [X0] :
( sQ226_spl
<=> ( ~ c_in(c_Pair(v_a____,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(v_a____,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)) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f8369,plain,
( ~ sQ1_spl
| ~ sQ212_spl
| ~ sQ10_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f8320,f8366,f1900,f7892,f1727]) ).
fof(f8394,plain,
! [X0,X1] :
( ~ sQ180_spl
| c_in(v_b____,X0,X1) ),
inference(resolution,[status(thm)],[f5976,f1666]) ).
fof(f8399,plain,
( sQ108_spl
| ~ sQ180_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3789,f8394]) ).
fof(f8410,plain,
( sQ108_spl
| ~ sQ180_spl ),
inference(contradiction_clause,[status(thm)],[f8399]) ).
fof(f8412,plain,
( ~ sQ178_spl
| $false ),
inference(resolution,[status(thm)],[f5932,f882]) ).
fof(f8427,plain,
~ sQ178_spl,
inference(contradiction_clause,[status(thm)],[f8412]) ).
fof(f8486,plain,
! [X0] :
( ~ sQ1_spl
| v_b____ = v_b____
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f1596,f3919]) ).
fof(f8487,plain,
! [X0] :
( ~ sQ1_spl
| v_b____ = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f1596,f4702]) ).
fof(f8488,plain,
! [X0] :
( ~ sQ127_spl
| v_b____ = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f1596,f4260]) ).
fof(f8490,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X1,tc_fun(X2,tc_bool)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f1596,f7409]) ).
fof(f8491,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Set_Oinsert(X1,v_F(v_P____),X2),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f1596,f5009]) ).
fof(f8492,plain,
! [X0] :
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(v_F(v_P____),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f1596,f4196]) ).
fof(f8505,definition,
! [X0] :
( sQ227_spl
<=> ( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f8508,plain,
( ~ sQ127_spl
| sQ17_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f8488,f8505,f2184,f4259]) ).
fof(f8513,definition,
! [X0] :
( sQ229_spl
<=> ( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f8516,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f8487,f8513,f2184,f1727]) ).
fof(f8521,definition,
! [X0] :
( sQ231_spl
<=> ( c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Relation_Orel__comp(c_Relation_Oconverse(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f8524,plain,
( ~ sQ1_spl
| sQ72_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f8486,f8521,f3184,f1727]) ).
fof(f8526,definition,
! [X0,X1,X2] :
( sQ232_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P____),X1,tc_fun(X2,tc_bool)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f8529,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f8490,f8526,f2184,f1727]) ).
fof(f8530,definition,
! [X0,X1,X2] :
( sQ233_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Set_Oinsert(X1,v_F(v_P____),X2),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f8533,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f8491,f8530,f2184,f1727]) ).
fof(f8535,definition,
! [X0] :
( sQ234_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(v_F(v_P____),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f8538,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f8492,f8535,f2184,f1727]) ).
fof(f8575,plain,
! [X0] :
( ~ sQ126_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f4257,f1596]) ).
fof(f8600,definition,
! [X0] :
( sQ235_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(hAPP(v_P____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f8603,plain,
( ~ sQ126_spl
| sQ17_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f8575,f8600,f2184,f4256]) ).
fof(f8675,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ126_spl
| v_b____ = v_a____
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ),
inference(resolution,[status(thm)],[f4336,f1596]) ).
fof(f8702,definition,
! [X0] :
( sQ237_spl
<=> ( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P____,v_b____,v_a____)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_b____ ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f8705,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ126_spl
| sQ17_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f8675,f8702,f2184,f4256,f1733,f1730]) ).
fof(f10557,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_a____ ),
inference(resolution,[status(thm)],[f3922,f4186]) ).
fof(f10562,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f3922,f1578]) ).
fof(f10567,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Relation_Otrans(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f3922,f1542]) ).
fof(f10582,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Relation_Oirrefl(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_b____ = v_a____ ),
inference(resolution,[status(thm)],[f3922,f1547]) ).
fof(f10587,definition,
! [X0] :
( sQ238_spl
<=> ~ c_Relation_Oirrefl(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f10590,plain,
( ~ sQ1_spl
| sQ238_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f10582,f2184,f10587,f1727]) ).
fof(f10591,definition,
! [X0] :
( sQ239_spl
<=> ( ~ c_Relation_Otrans(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| c_in(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f10594,plain,
( ~ sQ1_spl
| sQ239_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f10567,f2184,f10591,f1727]) ).
fof(f10595,definition,
! [X0] :
( sQ240_spl
<=> ~ c_Wellfounded_Owf(c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_b____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f10598,plain,
( ~ sQ1_spl
| sQ240_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f10562,f2184,f10595,f1727]) ).
fof(f10599,definition,
! [X0] :
( sQ241_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f10602,plain,
( ~ sQ1_spl
| sQ241_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f10557,f8346,f10599,f1727]) ).
fof(f10725,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_a____,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_a____ ),
inference(resolution,[status(thm)],[f3921,f4186]) ).
fof(f10730,plain,
( ~ sQ1_spl
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f3921,f1578]) ).
fof(f10750,plain,
( ~ sQ1_spl
| ~ c_Relation_Oirrefl(c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[f3921,f1547]) ).
fof(f10762,definition,
( sQ244_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_a____,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f10765,plain,
( ~ sQ1_spl
| sQ244_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f10725,f8346,f10762,f1727]) ).
fof(f10766,definition,
( sQ245_spl
<=> c_Relation_Oirrefl(c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f10769,plain,
( ~ sQ1_spl
| ~ sQ245_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f10750,f2184,f10766,f1727]) ).
fof(f10771,definition,
( sQ246_spl
<=> c_Wellfounded_Owf(c_Relation_Orel__comp(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(v_b____,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f10774,plain,
( ~ sQ1_spl
| ~ sQ246_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f10730,f2184,f10771,f1727]) ).
fof(f11015,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a____ = v_a____ ),
inference(resolution,[status(thm)],[f3920,f4186]) ).
fof(f11050,definition,
! [X0] :
( sQ247_spl
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P____),c_Relation_Orel__comp(c_Arrow__Order__Mirabelle_Omktop(X0,v_a____),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f11053,plain,
( ~ sQ1_spl
| sQ247_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f11015,f8346,f11050,f1727]) ).
fof(f11457,plain,
! [X0,X1] :
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f8172,f1596]) ).
fof(f11460,plain,
! [X0] :
( ~ sQ1_spl
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f8172,f1564]) ).
fof(f11484,definition,
! [X0,X1] :
( sQ248_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f11487,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f11457,f11484,f2184,f1727]) ).
fof(f11488,definition,
! [X0] :
( sQ249_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f11491,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f11460,f11488,f2184,f1727]) ).
fof(f12064,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
inference(paramodulation,[status(thm)],[f716,f886]) ).
fof(f12067,definition,
! [X0,X1] :
( sQ250_spl
<=> c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f12068,plain,
! [X0,X1] :
( ~ sQ250_spl
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
inference(component_clause,[status(thm)],[f12067]) ).
fof(f12070,definition,
! [X2] :
( sQ251_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,[sQ251_spl])],[split_symbol_definition]) ).
fof(f12073,plain,
( sQ251_spl
| sQ250_spl ),
inference(split_clause,[status(thm)],[f12064,f12067,f12070]) ).
fof(f12081,plain,
( ~ sQ250_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12068,f827]) ).
fof(f12082,plain,
~ sQ250_spl,
inference(contradiction_clause,[status(thm)],[f12081]) ).
fof(f13111,plain,
( ~ sQ1_spl
| ~ c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2325,f1562]) ).
fof(f13113,plain,
( ~ sQ1_spl
| c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Oantisym(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f2325,f1564]) ).
fof(f13118,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(X0,c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2325,f1542]) ).
fof(f13119,plain,
( ~ sQ1_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2325,f1542]) ).
fof(f13120,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[status(thm)],[f2325,f1542]) ).
fof(f13137,definition,
( sQ252_spl
<=> c_Relation_Oantisym(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f13139,plain,
( sQ252_spl
| ~ c_Relation_Oantisym(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f13137]) ).
fof(f13140,definition,
( sQ253_spl
<=> c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f13143,definition,
( sQ254_spl
<=> c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f13146,plain,
( ~ sQ1_spl
| sQ254_spl
| ~ sQ253_spl
| ~ sQ252_spl ),
inference(split_clause,[status(thm)],[f13113,f13137,f13140,f13143,f1727]) ).
fof(f13147,definition,
! [X0] :
( sQ255_spl
<=> ( ~ c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f13150,definition,
( sQ256_spl
<=> c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f13152,plain,
( sQ256_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f13150]) ).
fof(f13153,plain,
( ~ sQ1_spl
| ~ sQ256_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f13120,f13147,f13150,f1727]) ).
fof(f13154,plain,
( ~ sQ1_spl
| ~ sQ256_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f13119,f13140,f13150,f1727]) ).
fof(f13161,definition,
! [X0] :
( sQ258_spl
<=> ( ~ c_in(c_Pair(X0,c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| c_in(c_Pair(X0,c_Pair(v_b____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f13164,plain,
( ~ sQ1_spl
| ~ sQ256_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f13118,f13161,f13150,f1727]) ).
fof(f13171,definition,
( sQ260_spl
<=> c_Wellfounded_Owf(c_Relation_OId__on(c_Relation_OId__on(c_Relation_ORange(v_F(v_P____),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f13174,plain,
( ~ sQ1_spl
| ~ sQ253_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f13111,f13171,f13140,f1727]) ).
fof(f13176,plain,
( sQ256_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13152,f1434]) ).
fof(f13177,plain,
sQ256_spl,
inference(contradiction_clause,[status(thm)],[f13176]) ).
fof(f13178,plain,
( sQ252_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13139,f1437]) ).
fof(f13179,plain,
sQ252_spl,
inference(contradiction_clause,[status(thm)],[f13178]) ).
fof(f13265,plain,
! [X0,X1] :
( ~ sQ1_spl
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Oupper__semilattice__class_Osup(X0,v_F(v_P____),tc_fun(X1,tc_bool)),X1) ),
inference(resolution,[status(thm)],[f4738,f738]) ).
fof(f13269,plain,
! [X0,X1] :
( ~ sQ1_spl
| v_a____ = v_b____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Lattices_Oupper__semilattice__class_Osup(X1,v_F(v_P____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ),
inference(resolution,[status(thm)],[f13265,f1596]) ).
fof(f13272,plain,
! [X0] :
( ~ sQ1_spl
| v_a____ = v_b____
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Oupper__semilattice__class_Osup(X0,v_F(v_P____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,v_F(v_P____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[status(thm)],[f13265,f1564]) ).
fof(f13297,definition,
! [X0,X1] :
( sQ261_spl
<=> ( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(c_Lattices_Oupper__semilattice__class_Osup(X1,v_F(v_P____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = v_a____ ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f13300,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f13269,f13297,f2184,f1727]) ).
fof(f13301,definition,
! [X0] :
( sQ262_spl
<=> ( ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Lattices_Oupper__semilattice__class_Osup(X0,v_F(v_P____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X0,v_F(v_P____),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f13304,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f13272,f13301,f2184,f1727]) ).
fof(f13851,definition,
( sQ264_spl
<=> c_Relation_Otrans(c_Relation_OId__on(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f13853,plain,
( sQ264_spl
| ~ c_Relation_Otrans(c_Relation_OId__on(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f13851]) ).
fof(f13875,definition,
( sQ269_spl
<=> c_Relation_Oantisym(c_Relation_OId__on(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f13877,plain,
( sQ269_spl
| ~ c_Relation_Oantisym(c_Relation_OId__on(hAPP(v_P_H____,v_sko__CHAINED__1(v_P____,v_P_H____,v_a____,v_b____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f13875]) ).
fof(f13887,plain,
( sQ264_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13853,f1434]) ).
fof(f13888,plain,
sQ264_spl,
inference(contradiction_clause,[status(thm)],[f13887]) ).
fof(f13889,plain,
( sQ269_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13877,f1437]) ).
fof(f13890,plain,
sQ269_spl,
inference(contradiction_clause,[status(thm)],[f13889]) ).
fof(f15008,plain,
( ~ sQ110_spl
| c_in(c_Pair(v_b____,v_a____,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_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_b____,v_a____)),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_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f1675,f3799]) ).
fof(f15013,definition,
( sQ272_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_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f15014,plain,
( ~ sQ272_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_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f15013]) ).
fof(f15016,definition,
( sQ273_spl
<=> c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f15017,plain,
( ~ sQ273_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f15016]) ).
fof(f15018,plain,
( sQ273_spl
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(component_clause,[status(thm)],[f15016]) ).
fof(f15019,definition,
( sQ274_spl
<=> c_in(c_Pair(v_b____,v_a____,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,[sQ274_spl])],[split_symbol_definition]) ).
fof(f15020,plain,
( ~ sQ274_spl
| c_in(c_Pair(v_b____,v_a____,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)],[f15019]) ).
fof(f15022,plain,
( ~ sQ110_spl
| sQ274_spl
| sQ273_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f15008,f15013,f15016,f15019,f3798]) ).
fof(f15023,plain,
( ~ sQ274_spl
| sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15020,f1747]) ).
fof(f15024,plain,
( ~ sQ274_spl
| sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f15023]) ).
fof(f15025,plain,
( ~ sQ16_spl
| ~ sQ272_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_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f15014,f2182]) ).
fof(f15026,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ272_spl
| c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_sko__CHAINED__1(v_P_H____,v_P____,v_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f15014,f1749]) ).
fof(f15080,plain,
( ~ sQ16_spl
| ~ sQ272_spl
| ~ sQ26_spl
| ~ sQ273_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f15025,f15019,f15016,f2402,f15013,f2181]) ).
fof(f15093,plain,
( sQ273_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ272_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15018,f15026]) ).
fof(f15094,plain,
( sQ273_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ272_spl ),
inference(contradiction_clause,[status(thm)],[f15093]) ).
fof(f15095,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ273_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_b____,v_a____)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolution,[status(thm)],[f15017,f1783]) ).
fof(f15159,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ273_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f15095,f15013,f15016,f1733,f1730]) ).
fof(f15160,plain,
$false,
inference(sat_refutation,[status(thm)],[f1736,f1737,f1738,f1739,f1740,f1741,f1742,f1743,f1840,f1891,f1903,f1907,f2190,f2192,f2334,f2338,f2345,f2349,f2405,f2410,f2412,f2603,f2741,f2899,f2918,f2920,f3522,f3553,f3721,f3761,f3793,f3801,f3832,f3839,f3848,f3852,f3856,f4167,f4174,f4178,f4191,f4194,f4262,f4287,f4291,f4298,f4302,f4309,f4311,f4315,f4317,f4319,f4321,f4323,f4356,f4357,f4358,f4362,f4366,f4621,f4841,f4849,f4853,f4857,f4862,f5205,f5209,f5216,f5220,f5225,f5229,f5231,f5538,f5549,f5891,f5895,f5909,f5914,f5917,f5934,f5978,f7211,f7215,f7219,f7634,f7638,f7645,f7649,f7661,f7665,f7669,f7684,f7687,f7755,f7759,f7764,f7770,f7775,f7782,f7792,f7795,f7797,f7835,f7840,f7841,f7846,f7882,f7886,f7890,f7891,f7895,f7899,f7900,f8262,f8266,f8270,f8274,f8278,f8280,f8284,f8287,f8341,f8345,f8353,f8357,f8362,f8363,f8369,f8410,f8427,f8508,f8516,f8524,f8529,f8533,f8538,f8603,f8705,f10590,f10594,f10598,f10602,f10765,f10769,f10774,f11053,f11487,f11491,f12073,f12082,f13146,f13153,f13154,f13164,f13174,f13177,f13179,f13300,f13304,f13888,f13890,f15022,f15024,f15080,f15094,f15159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT069-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n010.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 04:30:10 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.26/0.51 % Drodi V4.1.1
% 227.07/29.23 % Refutation found
% 227.07/29.23 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 227.07/29.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 153.44/30.53 % Elapsed time: 29.876518 seconds
% 153.44/30.53 % CPU time: 206.657231 seconds
% 153.44/30.53 % Total memory used: 896.216 MB
% 153.44/30.53 % Net memory used: 839.269 MB
%------------------------------------------------------------------------------